Relevant bibliographies by topics / Stochastic ordinary differential equations

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Stochastic ordinary differential equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 4 February 2022

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Journal articles on the topic "Stochastic ordinary differential equations"

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Ünal, Gazanfer. "Stochastic symmetries of Wick type stochastic ordinary differential equations." International Journal of Modern Physics: Conference Series 38 (January 2015): 1560079. http://dx.doi.org/10.1142/s2010194515600794.

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We consider Wick type stochastic ordinary differential equations with Gaussian white noise. We define the stochastic symmetry transformations and Lie equations in Kondratiev space [Formula: see text]. We derive the determining system of Wick type stochastic partial differential equations with Gaussian white noise. Stochastic symmetries for stochastic Bernoulli, Riccati and general stochastic linear equation in [Formula: see text] are obtained. A stochastic version of canonical variables is also introduced.
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Deimling, K. "Sample solutions of stochastic ordinary differential equations∗." Stochastic Analysis and Applications 3, no. 1 (January 1985): 15–21. http://dx.doi.org/10.1080/07362998508809051.

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Ubøe, Jan. "Measurements of ordinary and stochastic differential equations." Stochastic Processes and their Applications 89, no. 2 (October 2000): 315–31. http://dx.doi.org/10.1016/s0304-4149(00)00026-0.

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Just, Wolfram, and Herwig Sauermann. "Ordinary differential equations for nonlinear stochastic oscillators." Physics Letters A 131, no. 4-5 (August 1988): 234–38. http://dx.doi.org/10.1016/0375-9601(88)90018-7.

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Luo, Peng, and Falei Wang. "Stochastic differential equations driven by G-Brownian motion and ordinary differential equations." Stochastic Processes and their Applications 124, no. 11 (November 2014): 3869–85. http://dx.doi.org/10.1016/j.spa.2014.07.004.

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Hiroshi, Kunita. "Convergence of stochastic flows connected with stochastic ordinary differential equations." Stochastics 17, no. 3 (May 1986): 215–51. http://dx.doi.org/10.1080/17442508608833391.

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Papanicolaou, G. C., and W. Kohler. "Asymptotic theory of mixing stochastic ordinary differential equations." Communications on Pure and Applied Mathematics 27, no. 5 (September 13, 2010): 641–68. http://dx.doi.org/10.1002/cpa.3160270503.

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Spigler, Renato. "Numerical simulation for certain stochastic ordinary differential equations." Journal of Computational Physics 74, no. 1 (January 1988): 244–62. http://dx.doi.org/10.1016/0021-9991(88)90079-4.

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Augustin, F., and P. Rentrop. "Stochastic Galerkin techniques for random ordinary differential equations." Numerische Mathematik 122, no. 3 (April 18, 2012): 399–419. http://dx.doi.org/10.1007/s00211-012-0466-8.

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Fredericks, E., and F. M. Mahomed. "Symmetries of th-Order Approximate Stochastic Ordinary Differential Equations." Journal of Applied Mathematics 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/263570.

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Symmetries of th-order approximate stochastic ordinary differential equations (SODEs) are studied. The determining equations of these SODEs are derived in an Itô calculus context. These determining equations are not stochastic in nature. SODEs are normally used to model nature (e.g., earthquakes) or for testing the safety and reliability of models in construction engineering when looking at the impact of random perturbations.
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Dissertations / Theses on the topic "Stochastic ordinary differential equations"

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Dalal, Nirav. "Applications of stochastic and ordinary differential equations to HIV dynamics." Thesis, University of Strathclyde, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.435132.

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LOBAO, WALDIR JESUS DE ARAUJO. "SOLUTION OF ORDINARY, PARTIAL AND STOCHASTIC DIFFERENTIAL EQUATIONS BY GENETIC PROGRAMMING AND AUTOMATIC DIFFERENTIATION." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=29824@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE EXCELENCIA ACADEMICA
O presente trabalho teve como objetivo principal investigar o potencial de algoritmos computacionais evolutivos, construídos a partir das técnicas de programação genética, combinados com diferenciação automática, na obtenção de soluções analíticas, exatas ou aproximadas, para problemas de equações diferenciais ordinárias (EDO), parciais (EDP) e estocásticas. Com esse intuito, e utilizando-se o ambiente de programação Matlab, diversos algoritmos foram elaborados e soluções analíticas de diferentes tipos de equações diferenciais foram determinadas. No caso das equações determinísticas, EDOs e EDPs, foram abordados problemas de diferentes graus de dificuldade, do básico até problemas complexos como o da equação do calor e a equação de Schrödinger para o átomo de hélio. Os resultados obtidos são promissores, com soluções exatas para a grande maioria dos problemas tratados e que atestam, empiricamente, a consistência e robustez da metodologia proposta. Com relação às equações estocásticas, o trabalho apresenta uma nova proposta de solução e metodologia alternativa para a precificação de opções europeias, de compra e de venda, e realiza algumas aplicações para o mercado brasileiro, com ações da Petrobras e da Vale. Além destas aplicações, são apresentadas as soluções de alguns modelos clássicos, usualmente utilizados na modelagem de preços e retornos de ativos financeiros, como, por exemplo, o movimento Browniano geométrico. De uma forma geral, os resultados obtidos nas aplicações indicam que a metodologia proposta nesta tese pode ser uma alternativa eficiente na modelagem de problemas científicos complexos.
The main objective of this work was to investigate the potential of evolutionary algorithms, built from genetic programming techniques and combined with automatic differentiation, in obtaining exact or approximate analytical solutions for problems of ordinary (ODE), partial (PDE), and stochastic differential equations. To this end, and using the Matlab programming environment, several algorithms were developed and analytical solutions of different types of differential equations were determined. In the case of deterministic equations, ODE and PDE problems of varying degrees of difficulty were discussed, from basic to complex problems such as the heat equation and the Schrödinger equation for the helium atom. The results are promising, including exact solutions for the vast majority of the problems treated, which attest empirically the consistency and robustness of the proposed methodology. Regarding the stochastic equations, the work presents a new proposal for a solution and alternative methodology for European options pricing, buying and selling, and performs some applications for the Brazilian market, with stock prices of Petrobras and Vale. In addition to these applications, there are presented solutions of some classical models, usually used in the modeling of prices and returns of financial assets, such as the geometric Brownian motion. In a general way, the results obtained in applications indicate that the methodology proposed in this dissertation can be an efficient alternative in modeling complex scientific problems.
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Moon, Kyoung-Sook. "Convergence rates of adaptive algorithms for deterministic and stochastic differential equations." Licentiate thesis, KTH, Numerical Analysis and Computer Science, NADA, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1382.

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Hahne, Jan [Verfasser]. "Waveform-relaxation methods for ordinary and stochastic differential equations with applications in distributed neural network simulations / Jan Hahne." Wuppertal : Universitätsbibliothek Wuppertal, 2018. http://d-nb.info/1164103385/34.

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Ding, Jie. "Structural and fluid analysis for large scale PEPA models, with applications to content adaptation systems." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/7975.

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The stochastic process algebra PEPA is a powerful modelling formalism for concurrent systems, which has enjoyed considerable success over the last decade. Such modelling can help designers by allowing aspects of a system which are not readily tested, such as protocol validity and performance, to be analysed before a system is deployed. However, model construction and analysis can be challenged by the size and complexity of large scale systems, which consist of large numbers of components and thus result in state-space explosion problems. Both structural and quantitative analysis of large scale PEPA models suffers from this problem, which has limited wider applications of the PEPA language. This thesis focuses on developing PEPA, to overcome the state-space explosion problem, and make it suitable to validate and evaluate large scale computer and communications systems, in particular a content adaption framework proposed by the Mobile VCE. In this thesis, a new representation scheme for PEPA is proposed to numerically capture the structural and timing information in a model. Through this numerical representation, we have found that there is a Place/Transition structure underlying each PEPA model. Based on this structure and the theories developed for Petri nets, some important techniques for the structural analysis of PEPA have been given. These techniques do not suffer from the state-space explosion problem. They include a new method for deriving and storing the state space and an approach to finding invariants which can be used to reason qualitatively about systems. In particular, a novel deadlock-checking algorithm has been proposed to avoid the state-space explosion problem, which can not only efficiently carry out deadlock-checking for a particular system but can tell when and how a system structure lead to deadlocks. In order to avoid the state-space explosion problem encountered in the quantitative analysis of a large scale PEPA model, a fluid approximation approach has recently been proposed, which results in a set of ordinary differential equations (ODEs) to approximate the underlying CTMC. This thesis presents an improved mapping from PEPA to ODEs based on the numerical representation scheme, which extends the class of PEPA models that can be subjected to fluid approximation. Furthermore, we have established the fundamental characteristics of the derived ODEs, such as the existence, uniqueness, boundedness and nonnegativeness of the solution. The convergence of the solution as time tends to infinity for several classes of PEPA models, has been proved under some mild conditions. For general PEPA models, the convergence is proved under a particular condition, which has been revealed to relate to some famous constants of Markov chains such as the spectral gap and the Log-Sobolev constant. This thesis has established the consistency between the fluid approximation and the underlying CTMCs for PEPA, i.e. the limit of the solution is consistent with the equilibrium probability distribution corresponding to a family of underlying density dependent CTMCs. These developments and investigations for PEPA have been applied to both qualitatively and quantitatively evaluate the large scale content adaptation system proposed by the Mobile VCE. These analyses provide an assessment of the current design and should guide the development of the system and contribute towards efficient working patterns and system optimisation.
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Robacker, Thomas C. "Comparison of Two Parameter Estimation Techniques for Stochastic Models." Digital Commons @ East Tennessee State University, 2015. https://dc.etsu.edu/etd/2567.

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Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a new method, the MCR method, which is unique to stochastic models and provides significantly better estimates and smaller confidence intervals for parameter values. Initial analysis of the new MCR method indicates that this method might be a viable method for parameter estimation for continuous time Markov chain models.
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Tribastone, Mirco. "Scalable analysis of stochastic process algebra models." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4629.

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The performance modelling of large-scale systems using discrete-state approaches is fundamentally hampered by the well-known problem of state-space explosion, which causes exponential growth of the reachable state space as a function of the number of the components which constitute the model. Because they are mapped onto continuous-time Markov chains (CTMCs), models described in the stochastic process algebra PEPA are no exception. This thesis presents a deterministic continuous-state semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying mathematics for the performance evaluation. This is suitable for models consisting of large numbers of replicated components, as the ODE problem size is insensitive to the actual population levels of the system under study. Furthermore, the ODE is given an interpretation as the fluid limit of a properly defined CTMC model when the initial population levels go to infinity. This framework allows the use of existing results which give error bounds to assess the quality of the differential approximation. The computation of performance indices such as throughput, utilisation, and average response time are interpreted deterministically as functions of the ODE solution and are related to corresponding reward structures in the Markovian setting. The differential interpretation of PEPA provides a framework that is conceptually analogous to established approximation methods in queueing networks based on meanvalue analysis, as both approaches aim at reducing the computational cost of the analysis by providing estimates for the expected values of the performance metrics of interest. The relationship between these two techniques is examined in more detail in a comparison between PEPA and the Layered Queueing Network (LQN) model. General patterns of translation of LQN elements into corresponding PEPA components are applied to a substantial case study of a distributed computer system. This model is analysed using stochastic simulation to gauge the soundness of the translation. Furthermore, it is subjected to a series of numerical tests to compare execution runtimes and accuracy of the PEPA differential analysis against the LQN mean-value approximation method. Finally, this thesis discusses the major elements concerning the development of a software toolkit, the PEPA Eclipse Plug-in, which offers a comprehensive modelling environment for PEPA, including modules for static analysis, explicit state-space exploration, numerical solution of the steady-state equilibrium of the Markov chain, stochastic simulation, the differential analysis approach herein presented, and a graphical framework for model editing and visualisation of performance evaluation results.
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Wang, Shuo. "Analysis and Application of Haseltine and Rawlings's Hybrid Stochastic Simulation Algorithm." Diss., Virginia Tech, 2016. http://hdl.handle.net/10919/82717.

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Stochastic effects in cellular systems are usually modeled and simulated with Gillespie's stochastic simulation algorithm (SSA), which follows the same theoretical derivation as the chemical master equation (CME), but the low efficiency of SSA limits its application to large chemical networks. To improve efficiency of stochastic simulations, Haseltine and Rawlings proposed a hybrid of ODE and SSA algorithm, which combines ordinary differential equations (ODEs) for traditional deterministic models and SSA for stochastic models. In this dissertation, accuracy analysis, efficient implementation strategies, and application of of Haseltine and Rawlings's hybrid method (HR) to a budding yeast cell cycle model are discussed. Accuracy of the hybrid method HR is studied based on a linear chain reaction system, motivated from the modeling practice used for the budding yeast cell cycle control mechanism. Mathematical analysis and numerical results both show that the hybrid method HR is accurate if either numbers of molecules of reactants in fast reactions are above certain thresholds, or rate constants of fast reactions are much larger than rate constants of slow reactions. Our analysis also shows that the hybrid method HR allows for a much greater region in system parameter space than those for the slow scale SSA (ssSSA) and the stochastic quasi steady state assumption (SQSSA) method. Implementation of the hybrid method HR requires a stiff ODE solver for numerical integration and an efficient event-handling strategy for slow reaction firings. In this dissertation, an event-handling strategy is developed based on inverse interpolation. Performances of five wildly used stiff ODE solvers are measured in three numerical experiments. Furthermore, inspired by the strategy of the hybrid method HR, a hybrid of ODE and SSA stochastic models for the budding yeast cell cycle is developed, based on a deterministic model in the literature. Simulation results of this hybrid model match very well with biological experimental data, and this model is the first to do so with these recently available experimental data. This study demonstrates that the hybrid method HR has great potential for stochastic modeling and simulation of large biochemical networks.
Ph. D.
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Bahník, Michal. "Stochastické obyčejné diferenciálni rovnice." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-232074.

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Diplomová práce se zabývá problematikou obyčejných stochastických diferenciálních rovnic. Po souhrnu teorie stochastických procesů, zejména tzv. Brownova pohybu je zaveden stochastický Itôův integrál, diferenciál a tzv. Itôova formule. Poté je definováno řešení počáteční úlohy stochastické diferenciální rovnice a uvedena věta o existenci a jednoznačnosti řešení. Pro případ lineární rovnice je odvozen tvar řešení a rovnice pro jeho střední hodnotu a rozptzyl. Závěr tvoří rozbor vybraných rovnic.
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MARINO, GISELA DORNELLES. "COMPLEX ORDINARY DIFFERENTIAL EQUATIONS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2007. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=10175@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
Neste texto estudamos diversos aspectos de singularidades de campos vetoriais holomorfos em dimensão 2. Discutimos detalhadamente o caso particular de uma singularidade sela-nó e o papel desempenhado pelas normalizações setoriais. Isto nos conduz à classificação analítica de difeomorfismos tangentes à identidade. seguir abordamos o Teorema de Seidenberg, tratando da redução de singularidades degeneradas em singularidades simples, através do procedimento de blow-up. Por fim, estudamos a demonstração do Teorema de Mattei-Moussu, acerca da existência de integrais primeiras para folheações holomorfas.
In the present text, we study the different aspects of singularities of holomorphic vector fields in dimension 2. We discuss in detail the particular case of a saddle-node singularity and the role of the sectorial normalizations. This leads us to the analytic classiffication of diffeomorphisms which are tangent to the identity. Next, we approach the Seidenberg Theorem, dealing with the reduction of degenerated singularities into simple ones, by means of the blow-up procedure. Finally, we study the proof of the well-known Mattei-Moussu Theorem concerning the existence of first integrals to holomorphic foliations.
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Books on the topic "Stochastic ordinary differential equations"

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Stochastic ordinary and stochastic partial differential equations: Transition from microscopic to macroscopic equations. New York: Springer Science+Business Media, 2008.

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An introduction to stochastic differential equations. Providence, Rhode Island: American Mathematical Society, 2013.

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Jamal, Najim, and SpringerLink (Online service), eds. Stochastic Analysis and Related Topics: In Honour of Ali Süleyman Üstünel, Paris, June 2010. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012.

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Herrmann, Samuel. Stochastic resonance: A mathematical approach in the small noise limit. Providence, Rhode Island: American Mathematical Society, 2014.

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Wu, Rangquan. Stochastic differential equations. Boston, Mass: Pitman Advanced, 1985.

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service), SpringerLink (Online, ed. Stochastic Differential Equations. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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Stochastic differential equations. Boston: Pitman Advanced Pub. Program, 1985.

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Sobczyk, Kazimierz. Stochastic Differential Equations. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3712-6.

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Cecconi, Jaures, ed. Stochastic Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-11079-5.

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Øksendal, Bernt. Stochastic Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-03620-4.

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Book chapters on the topic "Stochastic ordinary differential equations"

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Griffiths, David F., and Desmond J. Higham. "Stochastic Differential Equations." In Numerical Methods for Ordinary Differential Equations, 225–41. London: Springer London, 2010. http://dx.doi.org/10.1007/978-0-85729-148-6_16.

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Han, Xiaoying, and Peter E. Kloeden. "Stochastic Differential Equations." In Random Ordinary Differential Equations and Their Numerical Solution, 29–36. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6265-0_3.

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Holden, Helge, Bernt Øksendal, Jan Ubøe, and Tusheng Zhang. "Applications to Stochastic Ordinary Differential Equations." In Stochastic Partial Differential Equations, 115–57. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-89488-1_3.

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Holden, Helge, Bernt Øksendal, Jan Ubøe, and Tusheng Zhang. "Applications to stochastic ordinary differential equations." In Stochastic Partial Differential Equations, 105–40. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4684-9215-6_3.

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Grigoriu, Mircea. "Stochastic Ordinary Differential and Difference Equations." In Springer Series in Reliability Engineering, 237–335. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2327-9_7.

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Gliklikh, Yuri E. "Stochastic Differential Equations on Manifolds." In Ordinary and Stochastic Differential Geometry as a Tool for Mathematical Physics, 75–98. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8634-4_3.

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Mohammed, S. E. A. "Almost surely non-linear solutions of stochastic linear delay equations." In Ordinary and Partial Differential Equations, 270–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074735.

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Aubin, Jean-Pierre. "Viability Theorems for Ordinary and Stochastic Differential Equations." In Viability Theory, 19–52. Boston: Birkhäuser Boston, 2009. http://dx.doi.org/10.1007/978-0-8176-4910-4_3.

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Han, Xiaoying, and Peter E. Kloeden. "Taylor Expansions for Ordinary and Stochastic Differential Equations." In Random Ordinary Differential Equations and Their Numerical Solution, 61–72. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6265-0_6.

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Han, Xiaoying, and Peter E. Kloeden. "Numerical Methods for Ordinary and Stochastic Differential Equations." In Random Ordinary Differential Equations and Their Numerical Solution, 101–8. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-6265-0_9.

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Conference papers on the topic "Stochastic ordinary differential equations"

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Horváth Bokor, Rózsa. "On stability for numerical approximations of stochastic ordinary differential equations." In The 7'th Colloquium on the Qualitative Theory of Differential Equations. Szeged: Bolyai Institute, SZTE, 2003. http://dx.doi.org/10.14232/ejqtde.2003.6.15.

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Guias, Flavius. "Stochastic Simulation Method for Linearly Implicit Ordinary Differential Equations." In 2015 Second International Conference on Mathematics and Computers in Sciences and in Industry (MCSI). IEEE, 2015. http://dx.doi.org/10.1109/mcsi.2015.52.

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Liang, Yuxuan, Kun Ouyang, Hanshu Yan, Yiwei Wang, Zekun Tong, and Roger Zimmermann. "Modeling Trajectories with Neural Ordinary Differential Equations." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/207.

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Recent advances in location-acquisition techniques have generated massive spatial trajectory data. Recurrent Neural Networks (RNNs) are modern tools for modeling such trajectory data. After revisiting RNN-based methods for trajectory modeling, we expose two common critical drawbacks in the existing uses. First, RNNs are discrete-time models that only update the hidden states upon the arrival of new observations, which makes them an awkward fit for learning real-world trajectories with continuous-time dynamics. Second, real-world trajectories are never perfectly accurate due to unexpected sensor noise. Most RNN-based approaches are deterministic and thereby vulnerable to such noise. To tackle these challenges, we devise a novel method entitled TrajODE for more natural modeling of trajectories. It combines the continuous-time characteristic of Neural Ordinary Differential Equations (ODE) with the robustness of stochastic latent spaces. Extensive experiments on the task of trajectory classification demonstrate the superiority of our framework against the RNN counterparts.
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Mkhize, T. G., G. F. Oguis, K. Govinder, S. Moyo, and S. V. Meleshko. "Group classification of systems of two linear second-order stochastic ordinary differential equations." In MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5125077.

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Komori, Yoshio, Evelyn Buckwar, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Stochastic Runge-Kutta Methods with Deterministic High Order for Ordinary Differential Equations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637935.

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Guias, Flavius. "Stochastic Picard-Runge-Kutta Solvers for Large Systems of Autonomous Ordinary Differential Equations." In 2017 Fourth International Conference on Mathematics and Computers in Sciences and in Industry (MCSI). IEEE, 2017. http://dx.doi.org/10.1109/mcsi.2017.55.

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Bronstein, Manuel. "Linear ordinary differential equations." In Papers from the international symposium. New York, New York, USA: ACM Press, 1992. http://dx.doi.org/10.1145/143242.143264.

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Bournez, Olivier. "Ordinary Differential Equations & Computability." In 2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2018. http://dx.doi.org/10.1109/synasc.2018.00011.

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Wang, Xiong, and Riheng Jia. "Mean Field Equilibrium in Multi-Armed Bandit Game with Continuous Reward." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/429.

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Mean field game facilitates analyzing multi-armed bandit (MAB) for a large number of agents by approximating their interactions with an average effect. Existing mean field models for multi-agent MAB mostly assume a binary reward function, which leads to tractable analysis but is usually not applicable in practical scenarios. In this paper, we study the mean field bandit game with a continuous reward function. Specifically, we focus on deriving the existence and uniqueness of mean field equilibrium (MFE), thereby guaranteeing the asymptotic stability of the multi-agent system. To accommodate the continuous reward function, we encode the learned reward into an agent state, which is in turn mapped to its stochastic arm playing policy and updated using realized observations. We show that the state evolution is upper semi-continuous, based on which the existence of MFE is obtained. As the Markov analysis is mainly for the case of discrete state, we transform the stochastic continuous state evolution into a deterministic ordinary differential equation (ODE). On this basis, we can characterize a contraction mapping for the ODE to ensure a unique MFE for the bandit game. Extensive evaluations validate our MFE characterization, and exhibit tight empirical regret of the MAB problem.
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Damasceno, Berenice C., and Luciano Barbanti. "Ordinary fractional differential equations are in fact usual entire ordinary differential equations on time scales." In 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4904589.

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Reports on the topic "Stochastic ordinary differential equations"

1

Knorrenschild, M. Differential-algebraic equations as stiff ordinary differential equations. Office of Scientific and Technical Information (OSTI), May 1989. http://dx.doi.org/10.2172/6980335.

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2

Juang, Fen-Lien. Waveform methods for ordinary differential equations. Office of Scientific and Technical Information (OSTI), January 1990. http://dx.doi.org/10.2172/5005850.

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3

Aslam, S., and C. W. Gear. Asynchronous integration of ordinary differential equations on multiprocessors. Office of Scientific and Technical Information (OSTI), July 1989. http://dx.doi.org/10.2172/5979551.

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4

Dutt, Alok, Leslie Greengard, and Vladimir Rokhlin. Spectral Deferred Correction Methods for Ordinary Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, January 1998. http://dx.doi.org/10.21236/ada337779.

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5

Christensen, S. K., and G. Kallianpur. Stochastic Differential Equations for Neuronal Behavior. Fort Belvoir, VA: Defense Technical Information Center, June 1985. http://dx.doi.org/10.21236/ada159099.

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Herzog, K. J., M. D. Morris, and T. J. Mitchell. Bayesian approximation of solutions to linear ordinary differential equations. Office of Scientific and Technical Information (OSTI), November 1990. http://dx.doi.org/10.2172/6242347.

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7

Ober, Curtis C., Roscoe Bartlett, Todd S. Coffey, and Roger P. Pawlowski. Rythmos: Solution and Analysis Package for Differential-Algebraic and Ordinary-Differential Equations. Office of Scientific and Technical Information (OSTI), February 2017. http://dx.doi.org/10.2172/1364461.

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Dalang, Robert C., and N. Frangos. Stochastic Hyperbolic and Parabolic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, July 1994. http://dx.doi.org/10.21236/ada290372.

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Jiang, Bo, Roger Brockett, Weibo Gong, and Don Towsley. Stochastic Differential Equations for Power Law Behaviors. Fort Belvoir, VA: Defense Technical Information Center, January 2012. http://dx.doi.org/10.21236/ada577839.

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Sharp, D. H., S. Habib, and M. B. Mineev. Numerical Methods for Stochastic Partial Differential Equations. Office of Scientific and Technical Information (OSTI), July 1999. http://dx.doi.org/10.2172/759177.

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