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Relevant bibliographies by topics / Stochastic Delay Differential Equations

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Academic literature on the topic 'Stochastic Delay Differential Equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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Journal articles on the topic "Stochastic Delay Differential Equations"

1

Yang, Fang, Chen Fang, and Xu Sun. "Marcus Stochastic Differential Equations: Representation of Probability Density." Mathematics 12, no. 19 (2024): 2976. http://dx.doi.org/10.3390/math12192976.

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Marcus stochastic delay differential equations are often used to model stochastic dynamical systems with memory in science and engineering. It is challenging to study the existence, uniqueness, and probability density of Marcus stochastic delay differential equations, due to the fact that the delays cause very complicated correction terms. In this paper, we identify Marcus stochastic delay differential equations with some Marcus stochastic differential equations without delays but subject to extra constraints. This helps us to obtain the following two main results: (i) we establish a sufficien

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Tunc, Cemil, and Zozan Oktan. "STABILITY AND BOUNDEDNESS OF STOCHASTIC INTEGRO-DELAY DIFFERENTIAL EQUATIONS." Journal of Mathematical Analysis 15, no. 5 (2024): 69–83. https://doi.org/10.54379/jma-2024-5-5.

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This work addresses stochastic integro-delay differential equations (SIDDEs) of second order with two constant delays. In the study, two new results including sufficient conditions on stochastic asymptotic stability and stochastic boundedness in probability of solutions of the given SIDDEs are proved. The proofs of new results are done by using a Lyapunov-Krasovskii functional (L-KF) as a basic tool. To demonstrate the validity of the obtained results, two examples are provided. According to a comparison with previous literature, the results of this study are new and also allow new contributio

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Liu, Yue, Xuejing Meng, and Fuke Wu. "General Decay Stability for Stochastic Functional Differential Equations with Infinite Delay." International Journal of Stochastic Analysis 2010 (February 9, 2010): 1–17. http://dx.doi.org/10.1155/2010/875908.

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So far there are not many results on the stability for stochastic functional differential equations with infinite delay. The main aim of this paper is to establish some new criteria on the stability with general decay rate for stochastic functional differential equations with infinite delay. To illustrate the applications of our theories clearly, this paper also examines a scalar infinite delay stochastic functional differential equations with polynomial coefficients.

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Ma, Heping, Hui Jian, and Yu Shi. "A sufficient maximum principle for backward stochastic systems with mixed delays." Mathematical Biosciences and Engineering 20, no. 12 (2023): 21211–28. http://dx.doi.org/10.3934/mbe.2023938.

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<abstract><p>In this paper, we study the problem of optimal control of backward stochastic differential equations with three delays (discrete delay, moving-average delay and noisy memory). We establish the sufficient optimality condition for the stochastic system. We introduce two kinds of time-advanced stochastic differential equations as the adjoint equations, which involve the partial derivatives of the function $ f $ and its Malliavin derivatives. We also show that these two kinds of adjoint equations are equivalent. Finally, as applications, we discuss a linear-quadratic backw

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Petryna, G., and A. Stanzhytskyi. "APPROXIMATION OF STOCHASTIC DELAY DIFFERENTIAL SYSTEMS BY A STOCHASTIC SYSTEM WITHOUT DELAY." Bukovinian Mathematical Journal 12, no. 1 (2024): 120–36. http://dx.doi.org/10.31861/bmj2024.01.11.

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In this paper, we propose a scheme for approximating the solutions of stochastic differential equations with delay by solutions of stochastic differential equations without delay. Stochastic delay differential equations play a crucial role in modeling real-world processes where the evolution depends on past states, introducing complexities due to their infinite-dimensional phase space. To overcome these difficulties, we develop an approach based on approximating the delay system by an ordinary differential equation system of increased dimension. Our main result is to prove that, under certain

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Shevchenko, G. "Mixed stochastic delay differential equations." Theory of Probability and Mathematical Statistics 89 (January 26, 2015): 181–95. http://dx.doi.org/10.1090/s0094-9000-2015-00944-3.

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Pramila, G., and S. Ramadevi. "Time Delay and Mean Square Stochastic Differential Equations in Impetuous Stabilization." International Journal of Trend in Scientific Research and Development Volume-2, Issue-3 (2018): 627–31. http://dx.doi.org/10.31142/ijtsrd11062.

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Fofana, M. S. "Moment Lyapunov exponent of delay differential equations." International Journal of Mathematics and Mathematical Sciences 30, no. 6 (2002): 339–51. http://dx.doi.org/10.1155/s0161171202012103.

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The aim of this paper is to establish a connecting thread through the probabilistic concepts ofpth-moment Lyapunov exponents, the integral averaging method, and Hale's reduction approach for delay dynamical systems. We demonstrate this connection by studying the stability of perturbed deterministic and stochastic differential equations with fixed time delays in the displacement and derivative functions. Conditions guaranteeing stable and unstable solution response are derived. It is felt that the connecting thread provides a unified framework for the stability study of delay differential equat

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Wang, Peiguang, and Yan Xu. "Averaging Method for Neutral Stochastic Delay Differential Equations Driven by Fractional Brownian Motion." Journal of Function Spaces 2020 (May 29, 2020): 1–7. http://dx.doi.org/10.1155/2020/5212690.

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In this paper, we investigate the stochastic averaging method for neutral stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H∈1/2,1. By using the linear operator theory and the pathwise approach, we show that the solutions of neutral stochastic delay differential equations converge to the solutions of the corresponding averaged stochastic delay differential equations. At last, an example is provided to illustrate the applications of the proposed results.

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Ponosov, Arcady V. "Existence and uniqueness of solutions to stochastic fractional differential equations in multiple time scales." Russian Universities Reports. Mathematics, no. 141 (2023): 51–59. http://dx.doi.org/10.20310/2686-9667-2023-28-141-51-59.

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A novel class of nonlinear stochastic fractional differential equations with delay and the Jumarie and Ito differentials is introduced in the paper. The aim of the study is to prove existence and uniqueness of solutions to these equations. The main results of the paper generalise some previous findings made for the non-delay and three-scale equations under additional restrictions on the fractional order of the Jumarie differentials, which are removed in our analysis. The techniques used in the paper are based on the properties of the singular integral operators in specially designed spaces of

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Dissertations / Theses on the topic "Stochastic Delay Differential Equations"

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Bahar, Arifah. "Applications of stochastic differential equations and stochastic delay differential equations in population dynamics." Thesis, University of Strathclyde, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.415294.

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Reiss, Markus. "Nonparametric estimation for stochastic delay differential equations." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964782480.

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Reiß, Markus. "Nonparametric estimation for stochastic delay differential equations." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2002. http://dx.doi.org/10.18452/14741.

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Sei (X(t), t>= -r) ein stationärer stochastischer Prozess, der die affine stochastische Differentialgleichung mit Gedächtnis dX(t)=L(X(t+s))dt+sigma dW(t), t>= 0, löst, wobei sigma>0, (W(t), t>=0) eine Standard-Brownsche Bewegung und L ein stetiges lineares Funktional auf dem Raum der stetigen Funktionen auf [-r,0], dargestellt durch ein endliches signiertes Maß a, bezeichnet. Wir nehmen an, dass eine Trajektorie (X(t), -r 0, konvergiert. Diese Rate ist schlechter als in vielen klassischen Fällen. Wir beweisen jedoch eine untere Schranke, die zeigt, dass keine Schätzung eine bessere Rate im Mi

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Guillouzic, Steve. "Fokker-Planck approach to stochastic delay differential equations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58279.pdf.

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René, Alexandre. "Spectral Solution Method for Distributed Delay Stochastic Differential Equations." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34327.

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Stochastic delay differential equations naturally arise in models of complex natural phenomena, yet continue to resist efforts to find analytical solutions to them: general solutions are limited to linear systems with additive noise and a single delayed term. In this work we solve the case of distributed delays in linear systems with additive noise. Key to our solution is the development of a consistent interpretation for integrals over stochastic variables, obtained by means of a virtual discretization procedure. This procedure makes no assumption on the form of noise, and would likely be use

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Zhuang, Dawei. "Stability analysis of stochastic differential delay equations with jumps." Thesis, Swansea University, 2011. https://cronfa.swan.ac.uk/Record/cronfa42955.

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McDaniel, Austin James. "The Effects of Time Delay on Noisy Systems." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/556867.

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We consider a general stochastic differential delay equation (SDDE) with multiplicative colored noise. We study the limit as the time delays and the correlation times of the noises go to zero at the same rate. First, we derive the limiting equation for the equation obtained by Taylor expanding the SDDE to first order in the time delays. The limiting equation contains a noise-induced drift term that depends on the ratios of the time delays to the correlation times of the noises. We prove that, under appropriate assumptions, the solution of the equation obtained by the Taylor expansion converges

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Norton, Stewart J. "Noise induced changes to dynamic behaviour of stochastic delay differential equations." Thesis, University of Chester, 2008. http://hdl.handle.net/10034/72780.

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Kinnally, Michael Sean. "Stationary distributions for stochastic delay differential equations with non-negativity constraints." Diss., [La Jolla] : University of California, San Diego, 2009. http://wwwlib.umi.com/cr/ucsd/fullcit?p3355747.

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Thesis (Ph. D.)--University of California, San Diego, 2009.<br>Title from first page of PDF file (viewed June 23, 2009). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 114-116).

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McWilliams, Nairn Anthony. "Option pricing techniques under stochastic delay models." Thesis, University of Edinburgh, 2011. http://hdl.handle.net/1842/5754.

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The Black-Scholes model and corresponding option pricing formula has led to a wide and extensive industry, used by financial institutions and investors to speculate on market trends or to control their level of risk from other investments. From the formation of the Chicago Board Options Exchange in 1973, the nature of options contracts available today has grown dramatically from the single-date contracts considered by Black and Scholes (1973) to a wider and more exotic range of derivatives. These include American options, which can be exercised at any time up to maturity, as well as options ba

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Books on the topic "Stochastic Delay Differential Equations"

1

Mao, Xuerong. Exponential stability of stochastic differential equations. M. Dekker, 1994.

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Øksendal, Bernt. Stochastic Differential Equations. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02847-6.

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Øksendal, Bernt. Stochastic Differential Equations. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-662-03185-8.

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Øksendal, Bernt. Stochastic Differential Equations. Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-14394-6.

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Panik, Michael J. Stochastic Differential Equations. John Wiley & Sons, Inc., 2017. http://dx.doi.org/10.1002/9781119377399.

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Øksendal, Bernt. Stochastic Differential Equations. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-13050-6.

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Øksendal, Bernt. Stochastic Differential Equations. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-02574-1.

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

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9

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

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Øksendal, Bernt. Stochastic Differential Equations. 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 Delay Differential Equations"

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Longtin, André. "Stochastic Delay-Differential Equations." In Understanding Complex Systems. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02329-3_6.

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2

Rihan, Fathalla A. "Stochastic Delay Differential Equations." In Delay Differential Equations and Applications to Biology. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0626-7_7.

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an der Heiden, U. "Stochastic Properties of Simple Differential — Delay Equations." In Delay Equations, Approximation and Application. Birkhäuser Basel, 1985. http://dx.doi.org/10.1007/978-3-0348-7376-5_10.

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Kolmanovskii, V., and A. Myshkis. "Optimal control of stochastic delay systems." In Applied Theory of Functional Differential Equations. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8084-7_7.

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Kolmanovskii, V., and A. Myshkis. "State estimates of stochastic systems with delay." In Applied Theory of Functional Differential Equations. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8084-7_8.

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Küchler, Uwe, and Michael Sørensen. "Linear Stochastic Differential Equations with Time Delay." In Springer Series in Statistics. Springer New York, 1997. http://dx.doi.org/10.1007/0-387-22765-2_9.

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Bhat, Harish S. "Algorithms for Linear Stochastic Delay Differential Equations." In Springer Proceedings in Mathematics & Statistics. Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-2104-1_6.

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

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Rihan, Fathalla A. "Stochastic Delay Differential Model for Coronavirus Infection COVID-19." In Delay Differential Equations and Applications to Biology. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0626-7_13.

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Kolmanovskii, V., and A. Myshkis. "Optimal Control of Stochastic Delay Systems." In Introduction to the Theory and Applications of Functional Differential Equations. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-1965-0_15.

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Conference papers on the topic "Stochastic Delay Differential Equations"

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Sul, Jinhwan, Jungin E. Kim, and Yan Wang. "Quantum Functional Expansion to Solve Stochastic Differential Equations." In 2024 IEEE International Conference on Quantum Computing and Engineering (QCE). IEEE, 2024. https://doi.org/10.1109/qce60285.2024.00071.

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Guillouzic, Steve. "Transition rates for stochastic delay differential equations." In Stochastic and chaotic dynamics in the lakes. AIP, 2000. http://dx.doi.org/10.1063/1.1302421.

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Mensour, Boualem, and André Longtin. "Multistability and invariants in delay-differential equations." In Applied nonlinear dynamics and stochastic systems near the millenium. AIP, 1997. http://dx.doi.org/10.1063/1.54182.

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Kremliovsky, Michael N., and James B. Kadtke. "Using delay differential equations as dynamical classifiers." In Applied nonlinear dynamics and stochastic systems near the millenium. AIP, 1997. http://dx.doi.org/10.1063/1.54215.

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Griggs, Mitchell, Kevin Burrage, and Pamela Burrage. "Magnus methods for stochastic delay-differential equations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: ICNAAM2022. AIP Publishing, 2024. http://dx.doi.org/10.1063/5.0210336.

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RODKINA, A. "ON STABILITY OF STOCHASTIC NONLINEAR NON-AUTONOMOUS SYSTEMS WITH DELAY." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0198.

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Rosli, Norhayati, Arifah Bahar, S. H. Yeak, and Rahimah Jusoh@Awang. "2–stage stochastic Runge–Kutta for stochastic delay differential equations." In INTERNATIONAL CONFERENCE ON MATHEMATICS, ENGINEERING AND INDUSTRIAL APPLICATIONS 2014 (ICoMEIA 2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4915639.

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Ratchagit, Manlika, and Honglei Xu. "Parameter Identification of Stochastic Delay Differential Equations Using Differential Evolution." In 2022 37th International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC). IEEE, 2022. http://dx.doi.org/10.1109/itc-cscc55581.2022.9894864.

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GILSING, HAGEN. "ON ℒP-STABILITY OF NUMERICAL SCHEMES FOR LINEAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS". У Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0184.

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Khasawneh, Firas A., and Elizabeth Munch. "Exploring Equilibria in Stochastic Delay Differential Equations Using Persistent Homology." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35655.

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This paper explores the possibility of using techniques from topological data analysis for studying datasets generated from dynamical systems described by stochastic delay equations. The dataset is generated using Euler-Maryuama simulation for two first order systems with stochastic parameters drawn from a normal distribution. The first system contains additive noise whereas the second one contains parametric or multiplicative noise. Using Taken’s embedding, the dataset is converted into a point cloud in a high-dimensional space. Persistent homology is then employed to analyze the structure of

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Reports on the topic "Stochastic Delay Differential Equations"

1

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

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Gilsinn, David E. Approximating periodic solutions of autonomous delay differential equations. National Institute of Standards and Technology, 2006. http://dx.doi.org/10.6028/nist.ir.7375.

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Dalang, Robert C., and N. Frangos. Stochastic Hyperbolic and Parabolic Partial Differential Equations. Defense Technical Information Center, 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. Defense Technical Information Center, 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), 1999. http://dx.doi.org/10.2172/759177.

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

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Garrison, J. C. Stochastic differential equations and numerical simulation for pedestrians. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10184120.

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Xiu, Dongbin, and George E. Karniadakis. The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations. Defense Technical Information Center, 2003. http://dx.doi.org/10.21236/ada460654.

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

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Budhiraja, Amarjit, Paul Dupuis, and Arnab Ganguly. Moderate Deviation Principles for Stochastic Differential Equations with Jumps. Defense Technical Information Center, 2014. http://dx.doi.org/10.21236/ada616930.

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