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Relevant bibliographies by topics / Stochastic differential equations

Academic literature on the topic 'Stochastic differential equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 July 2024

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Dissertations / Theses
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Journal articles on the topic "Stochastic differential equations"

1

Norris, J. R., and B. Oksendal. "Stochastic Differential Equations." Mathematical Gazette 77, no. 480 (November 1993): 393. http://dx.doi.org/10.2307/3619809.

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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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Syed Tahir Hussainy and Pathmanaban K. "A study on analytical solutions for stochastic differential equations via martingale processes." Journal of Computational Mathematica 6, no. 2 (December 7, 2022): 85–92. http://dx.doi.org/10.26524/cm151.

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In this paper, we propose some analytical solutions of stochastic differential equations related to Martingale processes. In the first resolution, the answers of some stochastic differential equations are connected to other stochastic equations just with diffusion part (or drift free). The second suitable method is to convert stochastic differential equations into ordinary ones that it is tried to omit diffusion part of stochastic equation by applying Martingale processes. Finally, solution focuses on change of variable method that can be utilized about stochastic differential equations which are as function of Martingale processes like Wiener process, exponential Martingale process and differentiable processes.

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Halanay, A., T. Morozan, and C. Tudor. "Bounded solutions of affine stochastic differential equations and stability." Časopis pro pěstování matematiky 111, no. 2 (1986): 127–36. http://dx.doi.org/10.21136/cpm.1986.118271.

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MTW and H. Kunita. "Stochastic Flows and Stochastic Differential Equations." Journal of the American Statistical Association 93, no. 443 (September 1998): 1251. http://dx.doi.org/10.2307/2669903.

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Krylov, Nicolai. "Stochastic flows and stochastic differential equations." Stochastics and Stochastic Reports 51, no. 1-2 (November 1994): 155–58. http://dx.doi.org/10.1080/17442509408833949.

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Jacka, S. D., and H. Kunita. "Stochastic Flows and Stochastic Differential Equations." Journal of the Royal Statistical Society. Series A (Statistics in Society) 155, no. 1 (1992): 175. http://dx.doi.org/10.2307/2982680.

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Eliazar, Iddo. "Selfsimilar stochastic differential equations." Europhysics Letters 136, no. 4 (November 1, 2021): 40002. http://dx.doi.org/10.1209/0295-5075/ac4dd4.

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Abstract Diffusion in a logarithmic potential (DLP) attracted significant interest in physics recently. The dynamics of DLP are governed by a Langevin stochastic differential equation (SDE) whose underpinning potential is logarithmic, and that is driven by Brownian motion. The SDE that governs DLP is a particular case of a selfsimilar SDE: one that is driven by a selfsimilar motion, and that produces a selfsimilar motion. This paper establishes the pivotal role of selfsimilar SDEs via two novel universality results. I) Selfsimilar SDEs emerge universally, on the macro level, when applying scaling limits to micro-level SDEs. II) Selfsimilar SDEs emerge universally when applying the Lamperti transformation to stationary SDEs. Using the universality results, this paper further establishes: a novel statistical-analysis approach to selfsimilar Ito diffusions; and the focal importance of DLP.

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Malinowski, Marek T., and Mariusz Michta. "Stochastic set differential equations." Nonlinear Analysis: Theory, Methods & Applications 72, no. 3-4 (February 2010): 1247–56. http://dx.doi.org/10.1016/j.na.2009.08.015.

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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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Dissertations / Theses on the topic "Stochastic 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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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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Abourashchi, Niloufar. "Stability of stochastic differential equations." Thesis, University of Leeds, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509828.

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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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Hollingsworth, Blane Jackson Schmidt Paul G. "Stochastic differential equations a dynamical systems approach /." Auburn, Ala, 2008. http://repo.lib.auburn.edu/EtdRoot/2008/SPRING/Mathematics_and_Statistics/Dissertation/Hollingsworth_Blane_43.pdf.

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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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Rassias, Stamatiki. "Stochastic functional differential equations and applications." Thesis, University of Strathclyde, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.486536.

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The general truth that the principle of causality, that is, the future state of a system is independent of its past history, cannot support all the cases under consideration, leads to the introduction of the FDEs. However, the strong need of modelling real life problems, demands the inclusion of stochasticity. Thus, the appearance of the SFDEs (special case of which is the SDDEs) is necessary and definitely unavoidable. It has been almost a century since Langevin's model that the researchers incorporate noise terms into their work. Two of the main research interests are linked with the existence and uniqueness of the solution of the pertinent SFDE/SDDE which describes the problem under consideration, and the qualitative behaviour of the solution. This thesis, explores the SFDEs and their applications. According to the scientific literature, Ito's work (1940) contributed fundamentally into the formulation and study of the SFDEs. Khasminskii (1969), introduced a powerful test for SDEs to have non-explosion solutions without the satisfaction of the linear growth condition. Mao (2002), extended the idea so as to approach the SDDEs. However, Mao's test cannot be applied in specific types of SDDEs. Through our research work we establish an even more general Khasminskii-type test for SDDEs which covers a wide class of highly non-linear SDDEs. Following the proof of the non-explosion of the pertinent solution, we focus onto studying its qualitative behaviour by computing some moment and almost sure asymptotic estimations. In an attempt to apply and extend our theoretical results into real life problems we devote a big part of our research work into studying two very interesting problems that arise : from the area of the population dynamks and fromÃ‚Â·a problem related to the physical phenomenon of ENSO (EI Nino - Southern Oscillation)

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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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Curry, Charles. "Algebraic structures in stochastic differential equations." Thesis, Heriot-Watt University, 2014. http://hdl.handle.net/10399/2791.

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We define a new numerical integration scheme for stochastic differential equations driven by Levy processes with uniformly lower mean square remainder than that of the scheme of the same strong order of convergence obtained by truncating the stochastic Taylor series. In doing so we generalize recent results concerning stochastic differential equations driven by Wiener processes. The aforementioned works studied integration schemes obtained by applying an invertible mapping to the stochastic Taylor series, truncating the resulting series and applying the inverse of the original mapping. The shuffle Hopf algebra and its associated convolution algebra play important roles in the their analysis, arising from the combinatorial structure of iterated Stratonovich integrals. It was recently shown that the algebra generated by iterated It^o integrals of independent Levy processes is isomorphic to a quasi-shuffle algebra. We utilise this to consider map-truncate-invert schemes for Levy processes. To facilitate this, we derive a new form of stochastic Taylor expansion from those of Wagner & Platen, enabling us to extend existing algebraic encodings of integration schemes. We then derive an alternative method of computing map-truncate-invert schemes using a single step, resolving diffculties encountered at the inversion step in previous methods.

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Rajotte, Matthew. "Stochastic Differential Equations and Numerical Applications." VCU Scholars Compass, 2014. http://scholarscompass.vcu.edu/etd/3383.

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We will explore the topic of stochastic differential equations (SDEs) first by developing a foundation in probability theory and It\^o calculus. Formulas are then derived to simulate these equations analytically as well as numerically. These formulas are then applied to a basic population model as well as a logistic model and the various methods are compared. Finally, we will study a model for low dose anthrax exposure which currently implements a stochastic probabilistic uptake in a deterministic differential equation, and analyze how replacing the probablistic uptake with an SDE alters the dynamics.

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Books on the topic "Stochastic differential equations"

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

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

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Øksendal, Bernt. Stochastic Differential Equations. Berlin, Heidelberg: 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. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2017. http://dx.doi.org/10.1002/9781119377399.

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

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

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

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Book chapters on the topic "Stochastic differential equations"

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Doleans–Dade, C. "Stochastic Processes and Stochastic Differential Equations." In Stochastic Differential Equations, 5–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11079-5_1.

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Kallianpur, Gopinath, and Rajeeva L. Karandikar. "Stochastic Differential Equations." In Introduction to Option Pricing Theory, 79–93. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-0511-1_4.

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Øksendal, Bernt. "Stochastic Differential Equations." In Universitext, 35–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-662-02574-1_5.

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Protter, Philip. "Stochastic Differential Equations." In Stochastic Integration and Differential Equations, 187–284. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-662-02619-9_6.

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Gawarecki, Leszek, and Vidyadhar Mandrekar. "Stochastic Differential Equations." In Probability and Its Applications, 73–149. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-16194-0_3.

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Platen, Eckhard, and David Heath. "Stochastic Differential Equations." In A Benchmark Approach to Quantitative Finance, 237–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-47856-0_7.

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Rozanov, Yuriĭ A. "Stochastic Differential Equations." In Introduction to Random Processes, 68–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-72717-7_10.

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Kloeden, Peter E., and Eckhard Platen. "Stochastic Differential Equations." In Numerical Solution of Stochastic Differential Equations, 103–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-12616-5_4.

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Chung, K. L., and R. J. Williams. "Stochastic Differential Equations." In Introduction to Stochastic Integration, 217–64. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-9587-1_10.

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Schuss, Zeev. "Stochastic Differential Equations." In Applied Mathematical Sciences, 92–132. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-1605-1_4.

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Conference papers on the topic "Stochastic differential equations"

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Sharifi, J., and H. Momeni. "Optimal control equation for quantum stochastic differential equations." In 2010 49th IEEE Conference on Decision and Control (CDC). IEEE, 2010. http://dx.doi.org/10.1109/cdc.2010.5717172.

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MATICIUC, LUCIAN, and AUREL RĂŞCANU. "BACKWARD STOCHASTIC GENERALIZED VARIATIONAL INEQUALITY." In Applied Analysis and Differential Equations - The International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708229_0018.

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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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Kumar, Archana, and Pramod Kumar Kapur. "SRGMs Based on Stochastic Differential Equations." In 2009 Second International Conference on Communication Theory, Reliability, and Quality of Service (CTRQ). IEEE, 2009. http://dx.doi.org/10.1109/ctrq.2009.26.

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Malinowski, Marek T. "On Bipartite Fuzzy Stochastic Differential Equations." In 8th International Conference on Fuzzy Computation Theory and Applications. SCITEPRESS - Science and Technology Publications, 2016. http://dx.doi.org/10.5220/0006079501090114.

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Chen, Zengjing, and Xiangrong Wang. "Comonotonicity of Backward Stochastic Differential Equations." In Proceedings of the International Conference on Mathematical Finance. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812799579_0003.

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Megan, Mihail, Diana Monica Stoica, Diana Alina Bistrian, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Nonuniform Instability of Stochastic Differential Equations." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498498.

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FAGNOLA, FRANCO. "H-P QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS." In Proceedings of the RIMS Workshop on Infinite-Dimensional Analysis and Quantum Probability. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705242_0002.

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FAGNOLA, FRANCO. "REGULAR SOLUTIONS OF QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS." In Quantum Stochastics and Information - Statistics, Filtering and Control. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812832962_0002.

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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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Reports on the topic "Stochastic differential equations"

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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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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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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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Garrison, J. C. Stochastic differential equations and numerical simulation for pedestrians. Office of Scientific and Technical Information (OSTI), July 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. Fort Belvoir, VA: Defense Technical Information Center, January 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. Fort Belvoir, VA: Defense Technical Information Center, November 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. Fort Belvoir, VA: Defense Technical Information Center, January 2014. http://dx.doi.org/10.21236/ada616930.

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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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