Relevant bibliographies by topics / Stochastic partial 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 partial differential equations'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 August 2024

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Journal articles on the topic "Stochastic partial differential equations"

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BOUFOUSSI, B., and N. MRHARDY. "MULTIVALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS VIA BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 08, no. 02 (June 2008): 271–94. http://dx.doi.org/10.1142/s0219493708002317.

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In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic partial differential equation.
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Motamed, Mohammad. "Fuzzy-Stochastic Partial Differential Equations." SIAM/ASA Journal on Uncertainty Quantification 7, no. 3 (January 2019): 1076–104. http://dx.doi.org/10.1137/17m1140017.

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Barles, Guy, Rainer Buckdahn, and Etienne Pardoux. "Backward stochastic differential equations and integral-partial differential equations." Stochastics and Stochastic Reports 60, no. 1-2 (February 1997): 57–83. http://dx.doi.org/10.1080/17442509708834099.

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Fleming, W. H., and M. Nisio. "Differential games for stochastic partial differential equations." Nagoya Mathematical Journal 131 (September 1993): 75–107. http://dx.doi.org/10.1017/s0027763000004554.

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In this paper we are concerned with zero-sum two-player finite horizon games for stochastic partial differential equations (SPDE in short). The main aim is to formulate the principle of dynamic programming for the upper (or lower) value function and investigate the relationship between upper (or lower) value function and viscocity solution of min-max (or max-min) equation on Hilbert space.
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Ashyralyev, Allaberen, and Ülker Okur. "Stability of Stochastic Partial Differential Equations." Axioms 12, no. 7 (July 24, 2023): 718. http://dx.doi.org/10.3390/axioms12070718.

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In this paper, we study the stability of the stochastic parabolic differential equation with dependent coefficients. We consider the stability of an abstract Cauchy problem for the solution of certain stochastic parabolic differential equations in a Hilbert space. For the solution of the initial-boundary value problems (IBVPs), we obtain the stability estimates for stochastic parabolic equations with dependent coefficients in specific applications.
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Zhang, Qi, and Huaizhong Zhao. "Mass-conserving stochastic partial differential equations and backward doubly stochastic differential equations." Journal of Differential Equations 331 (September 2022): 1–49. http://dx.doi.org/10.1016/j.jde.2022.05.015.

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Zhu, QingFeng, and YuFeng Shi. "Forward-backward doubly stochastic differential equations and related stochastic partial differential equations." Science China Mathematics 55, no. 12 (May 20, 2012): 2517–34. http://dx.doi.org/10.1007/s11425-012-4411-1.

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BRZEŹNIAK, Z., M. CAPIŃSKI, and F. FLANDOLI. "STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND TURBULENCE." Mathematical Models and Methods in Applied Sciences 01, no. 01 (March 1991): 41–59. http://dx.doi.org/10.1142/s0218202591000046.

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Stochastic partial differential equations are proposed in order to model some turbulence phenomena. A particular case (the stochastic Burgers equations) is studied. Global existence of solutions is proved. Their regularity is also studied in detail. It is shown that the solutions cannot possess too high regularity.
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Bruned, Yvain, Martin Hairer, and Lorenzo Zambotti. "Renormalisation of Stochastic Partial Differential Equations." EMS Newsletter 2020-3, no. 115 (March 3, 2020): 7–11. http://dx.doi.org/10.4171/news/115/3.

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Pratelli, M., R. Carmona, and B. Rozovskii. "Stochastic Partial Differential Equations: Six Perspectives." Journal of the American Statistical Association 95, no. 450 (June 2000): 688. http://dx.doi.org/10.2307/2669432.

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Dissertations / Theses on the topic "Stochastic partial differential equations"

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Dareiotis, Anastasios Constantinos. "Stochastic partial differential and integro-differential equations." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/14186.

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In this work we present some new results concerning stochastic partial differential and integro-differential equations (SPDEs and SPIDEs) that appear in non-linear filtering. We prove existence and uniqueness of solutions of SPIDEs, we give a comparison principle and we suggest an approximation scheme for the non-local integral operators. Regarding SPDEs, we use techniques motivated by the work of De Giorgi, Nash, and Moser, in order to derive global and local supremum estimates, and a weak Harnack inequality.
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Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00916580.

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In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the second part, we consider hyperbolic conservation laws with stochastic forcing and study their approximations in the sense of Bhatnagar-Gross-Krook. In particular, we describe the conservation laws as a hydrodynamic limit of the stochastic BGK model as the microscopic scale vanishes. In the last part, we provide a new and fairly elementary proof of Skorkhod's classical theorem on existence of weak solutions to SDEs with continuous coefficients satisfying a suitable Lyapunov condition.
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Matetski, Kanstantsin. "Discretisations of rough stochastic partial differential equations." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/81460/.

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This thesis consists of two parts, in both of which we consider approximations of rough stochastic PDEs and investigate convergence properties of the approximate solutions. In the first part we use the theory of (controlled) rough paths to define a solution for one-dimensional stochastic PDEs of Burgers type driven by an additive space-time white noise. We prove that natural numerical approximations of these equations converge to the solution of a corrected continuous equation and that their optimal convergence rate in the uniform topology (in probability) is arbitrarily close to 1/2 . In the second part of the thesis we develop a general framework for spatial discretisations of parabolic stochastic PDEs whose solutions are provided in the framework of the theory of regularity structures and which are functions in time. As an application, we show that the dynamical �43 model on the dyadic grid converges after renormalisation to its continuous counterpart. This result in particular implies that, as expected, the �43 measure is invariant for this equation and that the lifetime of its solutions is almost surely infinite for almost every initial condition.
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Spantini, Alessio. "Preconditioning techniques for stochastic partial differential equations." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/82507.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2013.
This thesis was scanned as part of an electronic thesis pilot project.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 149-155).
This thesis is about preconditioning techniques for time dependent stochastic Partial Differential Equations arising in the broader context of Uncertainty Quantification. State-of-the-art methods for an efficient integration of stochastic PDEs require the solution field to lie on a low dimensional linear manifold. In cases when there is not such an intrinsic low rank structure we must resort on expensive and time consuming simulations. We provide a preconditioning technique based on local time stretching capable to either push or keep the solution field on a low rank manifold with substantial reduction in the storage and the computational burden. As a by-product we end up addressing also classical issues related to long time integration of stochastic PDEs.
by Alessio Spantini.
S.M.
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Prerapa, Surya Mohan. "Projection schemes for stochastic partial differential equations." Thesis, University of Southampton, 2009. https://eprints.soton.ac.uk/342800/.

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The focus of the present work is to develop stochastic reduced basis methods (SRBMs) for solving partial differential equations (PDEs) defined on random domains and nonlinear stochastic PDEs (SPDEs). SRBMs have been extended in the following directions: Firstly, an h-refinement strategy referred to as Multi-Element-SRBMs (ME-SRBMs) is developed for local refinement of the solution process. The random space is decomposed into subdomains where SRBMs are employed in each subdomain resulting in local response statistics. These local statistics are subsequently assimilated to compute the global statistics. Two types of preconditioning strategies namely global and local preconditioning strategies are discussed due to their merits such as degree of parallelizability and better convergence trends. The improved accuracy and convergence trends of ME-SRBMs are demonstrated by numerical investigation of stochastic steady state elasticity and stochastic heat transfer applications. The second extension involves the development of a computational approach employing SRBMs for solving linear elliptic PDEs defined on random domains. The key idea is to carry out spatial discretization of the governing equations using finite element (FE) methods and mesh deformation strategies. This results in a linear random algebraic system of equations whose coefficients of expansion can be computed nonintrusively either at the element or the global level. SRBMs are subsequently applied to the linear random algebraic system of equations to obtain the response statistics. We establish conditions that the input uncertainty model must satisfy to ensure the well-posedness of the problem. The proposed formulation is demonstrated on two and three dimensional model problems with uncertain boundaries undergoing steady state heat transfer. A large scale study involving a three-dimensional gas turbine model with uncertain boundary, has been presented in this context. Finally, a numerical scheme that combines SRBMs with the Picard iteration scheme is proposed for solving nonlinear SPDEs. The governing equations are linearized using the response process from the previous iteration and spatially discretized. The resulting linear random algebraic system of equations are solved to obtain the new response process which acts as a guess for the next iteration. These steps of linearization, spatial discretization, solving the system of equations and updating the current guess are repeated until the desired accuracy is achieved. The effectiveness and the limitations of the formulation are demonstrated employing numerical studies in nonlinear heat transfer and the one-dimensional Burger’s equation.
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Zhang, Qi. "Stationary solutions of stochastic partial differential equations and infinite horizon backward doubly stochastic differential equations." Thesis, Loughborough University, 2008. https://dspace.lboro.ac.uk/2134/34040.

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In this thesis we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between solutions of backward doubly stochastic differential equations (BDSDEs) on infinite horizon and the stationary solutions of the SPDEs. For this, we prove the existence and uniqueness of the L2ρ (Rd; R1) × L2ρ (Rd; Rd) valued solutions of BDSDEs with Lipschitz nonlinear term on both finite and infinite horizons, so obtain the solutions of initial value problems and the stationary weak solutions (independent of any initial value) of SPDEs. Also the L2ρ (Rd; R1) × L2ρ (Rd; Rd) valued BDSDE with non-Lipschitz term is considered. Moreover, we verify the time and space continuity of solutions of real-valued BDSDEs, so obtain the stationary stochastic viscosity solutions of real-valued SPDEs. The connection of the weak solutions of SPDEs and BDSDEs has independent interests in the areas of both SPDEs and BSDEs.
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Mu, Tingshu. "Backward stochastic differential equations and applications : optimal switching, stochastic games, partial differential equations and mean-field." Thesis, Le Mans, 2020. http://www.theses.fr/2020LEMA1023.

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Cette thèse est relative aux Equations Différentielles Stochastique Rétrogrades (EDSRs) réfléchies avec deux obstacles et leurs applications aux jeux de switching de somme nulle, aux systèmes d’équations aux dérivées partielles, aux problèmes de mean-field. Il y a deux parties dans cette thèse. La première partie porte sur le switching optimal stochastique et est composée de deux travaux. Dans le premier travail, nous montrons l’existence de la solution d’un système d’EDSR réfléchies à obstacles bilatéraux interconnectés dans le cadre probabiliste général. Ce problème est lié à un jeu de switching de somme nulle. Ensuite nous abordons la question de l’unicité de la solution. Et enfin nous appliquons les résultats obtenus pour montrer que le système d’EDP associé à une unique solution au sens viscosité, sans la condition de monotonie habituelle. Dans le second travail, nous considérons aussi un système d’EDSRs réfléchies à obstacles bilatéraux interconnectés dans le cadre markovien. La différence avec le premier travail réside dans le fait que le switching ne s’opère pas de la même manière. Cette fois-ci quand le switching est opéré, le système est mis dans l’état suivant importe peu lequel des joueurs décide de switcher. Cette différence est fondamentale et complique singulièrement le problème de l’existence de la solution du système. Néanmoins, dans le cadre markovien nous montrons cette existence et donnons un résultat d’unicité en utilisant principalement la méthode de Perron. Ensuite, le lien avec un jeu de switching spécifique est établi dans deux cadres. Dans la seconde partie nous étudions les EDSR réfléchies unidimensionnelles à deux obstacles de type mean-field. Par la méthode du point fixe, nous montrons l’existence et l’unicité de la solution dans deux cadres, en fonction de l’intégrabilité des données
This thesis is related to Doubly Reflected Backward Stochastic Differential Equations (DRBSDEs) with two obstacles and their applications in zero-sum stochastic switching games, systems of partial differential equations, mean-field problems.There are two parts in this thesis. The first part deals with optimal stochastic switching and is composed of two works. In the first work we prove the existence of the solution of a system of DRBSDEs with bilateral interconnected obstacles in a probabilistic framework. This problem is related to a zero-sum switching game. Then we tackle the problem of the uniqueness of the solution. Finally, we apply the obtained results and prove that, without the usual monotonicity condition, the associated PDE system has a unique solution in viscosity sense. In the second work, we also consider a system of DRBSDEs with bilateral interconnected obstacles in the markovian framework. The difference between this work and the first one lies in the fact that switching does not work in the same way. In this second framework, when switching is operated, the system is put in the following state regardless of which player decides to switch. This difference is fundamental and largely complicates the problem of the existence of the solution of the system. Nevertheless, in the Markovian framework we show this existence and give a uniqueness result by the Perron’s method. Later on, two particular switching games are analyzed.In the second part we study a one-dimensional Reflected BSDE with two obstacles of mean-field type. By the fixed point method, we show the existence and uniqueness of the solution in connection with the integrality of the data
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Athreya, Siva. "Probability and semilinear partial differential equations /." Thesis, Connect to this title online; UW restricted, 1998. http://hdl.handle.net/1773/5799.

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Pätz, Torben [Verfasser]. "Segmentation of Stochastic Images using Stochastic Partial Differential Equations / Torben Pätz." Bremen : IRC-Library, Information Resource Center der Jacobs University Bremen, 2012. http://d-nb.info/1035219735/34.

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Pak, Alexey. "Stochastic partial differential equations with coefficients depending on VaR." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/93458/.

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In this paper we prove the well-posedness for a stochastic partial differential equation (SPDE) whose solution is a probability-measure-valued process. We allow the coefficients to depend on the median or, more generally, on the γ-quantile (or some its useful extensions) of the underlying distribution. Such SPDEs arise in many applications, for example, in auction system described in [2]. The well-posedness of this SPDE does not follow by standard arguments because the γ-quantile is not a continuous function on the space of probability measures equipped with the weak convergence.
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Books on the topic "Stochastic partial differential equations"

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Pardoux, Étienne. Stochastic Partial Differential Equations. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89003-2.

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Holden, Helge, Bernt Øksendal, Jan Ubøe, and Tusheng Zhang. Stochastic Partial Differential Equations. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-89488-1.

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Lototsky, Sergey V., and Boris L. Rozovsky. Stochastic Partial Differential Equations. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-58647-2.

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Holden, Helge, Bernt Øksendal, Jan Ubøe, and Tusheng Zhang. Stochastic Partial Differential Equations. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4684-9215-6.

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Alison, Etheridge, ed. Stochastic partial differential equations. Cambridge: Cambridge University Press, 1995.

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Pardoux, Etienne, and Aurel Rӑşcanu. Stochastic Differential Equations, Backward SDEs, Partial Differential Equations. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05714-9.

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

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Carmona, Rene, and Boris Rozovskii, eds. Stochastic Partial Differential Equations: Six Perspectives. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/surv/064.

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Da Prato, Giuseppe, and Luciano Tubaro, eds. Stochastic Partial Differential Equations and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0072879.

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Chen, Gui-Qiang, Elton Hsu, and Mark Pinsky, eds. Stochastic Analysis and Partial Differential Equations. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/conm/429.

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Book chapters on the topic "Stochastic partial differential equations"

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Holden, Helge, Bernt Øksendal, Jan Ubøe, and Tusheng Zhang. "Stochastic partial differential equations." In Stochastic Partial Differential Equations, 141–91. Boston, MA: Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4684-9215-6_4.

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Langtangen, H. P., and H. Osnes. "Stochastic Partial Differential Equations." In Lecture Notes in Computational Science and Engineering, 257–320. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-18237-2_7.

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Bovier, Anton, and Frank den Hollander. "Stochastic Partial Differential Equations." In Metastability, 305–21. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-24777-9_12.

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Funaki, Tadahisa. "Stochastic Partial Differential Equations." In Lectures on Random Interfaces, 81–92. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-0849-8_3.

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Friz, Peter K., and Martin Hairer. "Stochastic Partial Differential Equations." In Universitext, 169–90. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08332-2_12.

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Grigoriu, Mircea. "Stochastic Partial Differential Equations." In Springer Series in Reliability Engineering, 379–454. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2327-9_9.

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Lang, Annika. "Stochastic Partial Differential Equations." In Computer Vision, 770–75. Boston, MA: Springer US, 2014. http://dx.doi.org/10.1007/978-0-387-31439-6_681.

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Friz, Peter K., and Martin Hairer. "Stochastic partial differential equations." In Universitext, 207–42. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41556-3_12.

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Lang, Annika. "Stochastic Partial Differential Equations." In Computer Vision, 1212–17. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-63416-2_681.

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Lang, Annika. "Stochastic Partial Differential Equations." In Computer Vision, 1–6. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-03243-2_681-1.

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Conference papers on the topic "Stochastic partial differential equations"

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Alexander, Francis J. "Algorithm Refinement for Stochastic Partial Differential Equations." In RAREFIED GAS DYNAMICS: 23rd International Symposium. AIP, 2003. http://dx.doi.org/10.1063/1.1581638.

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Zhang, Lei, Yongsheng Ding, Kuangrong Hao, and Tong Wang. "Controllability of impulsive fractional stochastic partial differential equations." In 2013 10th IEEE International Conference on Control and Automation (ICCA). IEEE, 2013. http://dx.doi.org/10.1109/icca.2013.6564989.

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HESSE, CHRISTIAN H. "A STOCHASTIC METHODOLOGY FOR NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS." In Proceedings of the Fourth International Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814291071_0044.

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Guo, Zhenwei, Xiangping Hu, and Jianxin Liu. "Modelling magnetic field data using stochastic partial differential equations." In International Conference on Engineering Geophysics, Al Ain, United Arab Emirates, 9-12 October 2017. Society of Exploration Geophysicists, 2017. http://dx.doi.org/10.1190/iceg2017-030.

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Grigo, Constantin, and Phaedon-Stelios Koutsourelakis. "PROBABILISTIC REDUCED-ORDER MODELING FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS." In 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2017. http://dx.doi.org/10.7712/120217.5356.16731.

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Khasilev, Vladimir. "Optimal control of wave propagation governed by nonlinear partial differential equations." In Applied nonlinear dynamics and stochastic systems near the millenium. AIP, 1997. http://dx.doi.org/10.1063/1.54191.

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Wang, Guangchen, Zhen Wu, and Jie Xiong. "Partial information LQ optimal control of backward stochastic differential equations." In 2012 10th World Congress on Intelligent Control and Automation (WCICA 2012). IEEE, 2012. http://dx.doi.org/10.1109/wcica.2012.6358150.

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Guiaş, Flavius. "Improved stochastic approximation methods for discretized parabolic partial differential equations." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2016 (ICCMSE 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4968683.

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Potsepaev, R., and C. L. Farmer. "Application of Stochastic Partial Differential Equations to Reservoir Property Modelling." In 12th European Conference on the Mathematics of Oil Recovery. Netherlands: EAGE Publications BV, 2010. http://dx.doi.org/10.3997/2214-4609.20144964.

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Kolarova, Edita, and Lubomir Brancik. "Noise Influenced Transmission Line Model via Partial Stochastic Differential Equations." In 2019 42nd International Conference on Telecommunications and Signal Processing (TSP). IEEE, 2019. http://dx.doi.org/10.1109/tsp.2019.8769101.

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Reports on the topic "Stochastic partial differential equations"

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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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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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Jones, Richard H. Fitting Stochastic Partial Differential Equations to Spatial Data. Fort Belvoir, VA: Defense Technical Information Center, September 1993. http://dx.doi.org/10.21236/ada279870.

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Chow, Pao-Liu, and Jose-Luis Menaldi. Stochastic Partial Differential Equations in Physical and Systems Sciences. Fort Belvoir, VA: Defense Technical Information Center, November 1986. http://dx.doi.org/10.21236/ada175400.

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Webster, Clayton G., Guannan Zhang, and Max D. Gunzburger. An adaptive wavelet stochastic collocation method for irregular solutions of stochastic partial differential equations. Office of Scientific and Technical Information (OSTI), October 2012. http://dx.doi.org/10.2172/1081925.

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Preston, Leiph, and Christian Poppeliers. LDRD #218329: Uncertainty Quantification of Geophysical Inversion Using Stochastic Partial Differential Equations. Office of Scientific and Technical Information (OSTI), September 2021. http://dx.doi.org/10.2172/1819413.

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Glimm, James, Yuefan Deng, W. Brent Lindquist, and Folkert Tangerman. Final report: Stochastic partial differential equations applied to the predictability of complex multiscale phenomena. Office of Scientific and Technical Information (OSTI), August 2001. http://dx.doi.org/10.2172/771242.

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Webster, Clayton, Raul Tempone, and Fabio Nobile. The analysis of a sparse grid stochastic collocation method for partial differential equations with high-dimensional random input data. Office of Scientific and Technical Information (OSTI), December 2007. http://dx.doi.org/10.2172/934852.

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Trenchea, Catalin. Efficient Numerical Approximations of Tracking Statistical Quantities of Interest From the Solution of High-Dimensional Stochastic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada567709.

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10

Trenchea, Catalin. Efficient Numerical Approximations of Tracking Statistical Quantities of Interest From the Solution of High-Dimensional Stochastic Partial Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada577122.

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