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Journal articles on the topic 'Stochastic partial differential equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Da Prato, G., and L. Tubaro. "Fully Nonlinear Stochastic Partial Differential Equations." SIAM Journal on Mathematical Analysis 27, no. 1 (January 1996): 40–55. http://dx.doi.org/10.1137/s0036141093256769.

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12

Allen, Edward J. "Derivation of Stochastic Partial Differential Equations." Stochastic Analysis and Applications 26, no. 2 (March 7, 2008): 357–78. http://dx.doi.org/10.1080/07362990701857319.

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13

Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations." Stochastic Processes and their Applications 123, no. 12 (December 2013): 4294–336. http://dx.doi.org/10.1016/j.spa.2013.06.015.

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14

Chen, Zhen-Qing, Kyeong-Hun Kim, and Panki Kim. "Fractional time stochastic partial differential equations." Stochastic Processes and their Applications 125, no. 4 (April 2015): 1470–99. http://dx.doi.org/10.1016/j.spa.2014.11.005.

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15

Lions, Pierre-Louis, and Panagiotis E. Souganidis. "Fully nonlinear stochastic partial differential equations." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 326, no. 9 (May 1998): 1085–92. http://dx.doi.org/10.1016/s0764-4442(98)80067-0.

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16

Di Nunno, Giulia, and Tusheng Zhang. "Approximations of stochastic partial differential equations." Annals of Applied Probability 26, no. 3 (June 2016): 1443–66. http://dx.doi.org/10.1214/15-aap1122.

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17

BAKHTIN, YURI, and JONATHAN C. MATTINGLY. "STATIONARY SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH MEMORY AND STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS." Communications in Contemporary Mathematics 07, no. 05 (October 2005): 553–82. http://dx.doi.org/10.1142/s0219199705001878.

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We explore Itô stochastic differential equations where the drift term possibly depends on the infinite past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proven if the dependence on the past decays sufficiently fast. The results of this paper are then applied to stochastically forced dissipative partial differential equations such as the stochastic Navier–Stokes equation and stochastic Ginsburg–Landau equation.

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18

Buckdahn, Rainer, and Shige Peng. "Stationary backward stochastic differential equations and associated partial differential equations." Probability Theory and Related Fields 115, no. 3 (1999): 383. http://dx.doi.org/10.1007/s004400050242.

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19

Zhu, Jie. "The Mean Field Forward Backward Stochastic Differential Equations and Stochastic Partial Differential Equations." Pure and Applied Mathematics Journal 4, no. 3 (2015): 120. http://dx.doi.org/10.11648/j.pamj.20150403.20.

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20

Zhu, Qingfeng, and Yufeng Shi. "Backward doubly stochastic differential equations with jumps and stochastic partial differential-integral equations." Chinese Annals of Mathematics, Series B 33, no. 1 (January 2012): 127–42. http://dx.doi.org/10.1007/s11401-011-0686-8.

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21

Buckdahn, Rainer, Juan Li, and Shige Peng. "Mean-field backward stochastic differential equations and related partial differential equations." Stochastic Processes and their Applications 119, no. 10 (October 2009): 3133–54. http://dx.doi.org/10.1016/j.spa.2009.05.002.

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22

Wu, Jinbiao. "Stochastic viscosity solutions for stochastic integral-partial differential equations." Journal of Mathematical Physics 62, no. 2 (February 1, 2021): 021501. http://dx.doi.org/10.1063/5.0019229.

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23

Ocone, Daniel. "Stochastic calculus of variations for stochastic partial differential equations." Journal of Functional Analysis 79, no. 2 (August 1988): 288–331. http://dx.doi.org/10.1016/0022-1236(88)90015-8.

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24

Hochberg, David, Carmen Molina-París, Juan Pérez-Mercader, and Matt Visser. "Effective action for stochastic partial differential equations." Physical Review E 60, no. 6 (December 1, 1999): 6343–60. http://dx.doi.org/10.1103/physreve.60.6343.

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25

Nagase, Noriaki, and Makiko Nisio. "Optimal Controls for Stochastic Partial Differential Equations." SIAM Journal on Control and Optimization 28, no. 1 (January 1990): 186–213. http://dx.doi.org/10.1137/0328010.

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26

Lord, Gabriel J., and Tony Shardlow. "Postprocessing for Stochastic Parabolic Partial Differential Equations." SIAM Journal on Numerical Analysis 45, no. 2 (January 2007): 870–89. http://dx.doi.org/10.1137/050640138.

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27

LU, KENING, and BJÖRN SCHMALFUß. "INVARIANT FOLIATIONS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS." Stochastics and Dynamics 08, no. 03 (September 2008): 505–18. http://dx.doi.org/10.1142/s0219493708002421.

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In this paper, we study the existence of an invariant foliation for a class of stochastic partial differential equations with a multiplicative white noise. This invariant foliation is used to trace the long term behavior of all solutions of these equations.

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28

Schmalfuss, Bj�rn, Kening Lu, and Jinqiao Duan. "Invariant manifolds for stochastic partial differential equations." Annals of Probability 31, no. 4 (October 2003): 2109–35. http://dx.doi.org/10.1214/aop/1068646380.

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29

Lindstr⊘m, Tom, Bernt Øksendal, Jan Ub⊘e, and Tusheng Zhang. "Stability properties of stochastic partial differential equations." Stochastic Analysis and Applications 13, no. 2 (January 1995): 177–204. http://dx.doi.org/10.1080/07362999508809390.

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30

Mijena, Jebessa B., and Erkan Nane. "Space–time fractional stochastic partial differential equations." Stochastic Processes and their Applications 125, no. 9 (September 2015): 3301–26. http://dx.doi.org/10.1016/j.spa.2015.04.008.

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31

Gy�ngy, Istv�n. "Stochastic partial differential equations on manifolds,I." Potential Analysis 2, no. 2 (June 1993): 101–13. http://dx.doi.org/10.1007/bf01049295.

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32

Prohl, Andreas, and Christian Schellnegger. "Adaptive Concepts for Stochastic Partial Differential Equations." Journal of Scientific Computing 80, no. 1 (March 28, 2019): 444–74. http://dx.doi.org/10.1007/s10915-019-00944-z.

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33

Babuška, Ivo, and Panagiotis Chatzipantelidis. "On solving elliptic stochastic partial differential equations." Computer Methods in Applied Mechanics and Engineering 191, no. 37-38 (August 2002): 4093–122. http://dx.doi.org/10.1016/s0045-7825(02)00354-7.

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34

Krylov, N. V. "Hörmander’s theorem for stochastic partial differential equations." St. Petersburg Mathematical Journal 27, no. 3 (March 30, 2016): 461–79. http://dx.doi.org/10.1090/spmj/1398.

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35

Øksendal, Bernt. "Optimal Control of Stochastic Partial Differential Equations." Stochastic Analysis and Applications 23, no. 1 (January 19, 2005): 165–79. http://dx.doi.org/10.1081/sap-200044467.

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36

Debussche, Arnaud, and Boris Rozovsky. "Stochastic partial differential equations: analysis and computations." Stochastic Partial Differential Equations: Analysis and Computations 1, no. 1 (March 2013): 1–2. http://dx.doi.org/10.1007/s40072-013-0009-z.

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37

Gy�ngy, I., and E. Pardoux. "On quasi-linear stochastic partial differential equations." Probability Theory and Related Fields 94, no. 4 (December 1993): 413–25. http://dx.doi.org/10.1007/bf01192556.

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38

Kumar, P., T. E. Unny, and K. Ponnambalam. "Stochastic partial differential equations in groundwater hydrology." Stochastic Hydrology and Hydraulics 5, no. 3 (September 1991): 239–51. http://dx.doi.org/10.1007/bf01544060.

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39

Unny, T. E. "Stochastic partial differential equations in groundwater hydrology." Stochastic Hydrology and Hydraulics 3, no. 2 (June 1989): 135–53. http://dx.doi.org/10.1007/bf01544077.

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40

Zhang, Xicheng. "Regularities for semilinear stochastic partial differential equations." Journal of Functional Analysis 249, no. 2 (August 2007): 454–76. http://dx.doi.org/10.1016/j.jfa.2007.03.018.

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41

Seeβelberg, Markus, and Francesco Petruccione. "Numerical integration of stochastic partial differential equations." Computer Physics Communications 74, no. 3 (March 1993): 303–15. http://dx.doi.org/10.1016/0010-4655(93)90014-4.

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42

Alexander, Francis J., Alejandro L. Garcia, and Daniel M. Tartakovsky. "Algorithm Refinement for Stochastic Partial Differential Equations." Journal of Computational Physics 182, no. 1 (October 2002): 47–66. http://dx.doi.org/10.1006/jcph.2002.7149.

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43

Roth, Ch. "Difference Methods for Stochastic Partial Differential Equations." ZAMM 82, no. 11-12 (November 2002): 821–30. http://dx.doi.org/10.1002/1521-4001(200211)82:11/12<821::aid-zamm821>3.0.co;2-l.

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44

Zhu, Qingfeng, and Yufeng Shi. "Mean-Field Forward-Backward Doubly Stochastic Differential Equations and Related Nonlocal Stochastic Partial Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/194341.

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Mean-field forward-backward doubly stochastic differential equations (MF-FBDSDEs) are studied, which extend many important equations well studied before. Under some suitable monotonicity assumptions, the existence and uniqueness results for measurable solutions are established by means of a method of continuation. Furthermore, the probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations (SPDEs) combined with algebra equations is given.

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45

Veraar, Mark C. "Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations." Journal of Evolution Equations 10, no. 1 (October 3, 2009): 85–127. http://dx.doi.org/10.1007/s00028-009-0041-7.

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46

Du, Kai, and Qi Zhang. "Semi-linear degenerate backward stochastic partial differential equations and associated forward–backward stochastic differential equations." Stochastic Processes and their Applications 123, no. 5 (May 2013): 1616–37. http://dx.doi.org/10.1016/j.spa.2013.01.005.

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47

Essaky, El Hassan, and Youssef Ouknine. "Homogenization of Multivalued Partial Differential Equations via Reflected Backward Stochastic Differential Equations." Stochastic Analysis and Applications 22, no. 1 (January 2004): 81–98. http://dx.doi.org/10.1081/sap-120028024.

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48

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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49

Duan, Pengju. "SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions." Journal of Function Spaces 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/5916132.

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The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. We prove the existence and uniqueness of the solutions to the backward stochastic differential equations by constructing Cauchy sequence and fixed point theorem. Moreover, we give a probabilistic solution of stochastic partial differential integral equations by means of the solution of backward stochastic differential equations. Finally, we give an example to illustrate.

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50

Matthies, H. G. "Stochastic finite elements: Computational approaches to stochastic partial differential equations." ZAMM 88, no. 11 (November 3, 2008): 849–73. http://dx.doi.org/10.1002/zamm.200800095.

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