Articles on Stochastic partial 
differential equations 

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Here is a list of research papers related  to stochastic partial differential equations (SPDEs) and their applications.
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Here is a MATH SCINET link to a general bibliography on stochastic PDEs. If you are interested in more specific topics, you can find a subject index below.

Subject index:

  • General theory

  • General results on existence and uniqueness of solutions

  • Parabolic SPDEs and stochastic heat equation.

  • Hyperbolic SPDEs and the stochastie wave equation

  • SPDEs and non linear filtering.

  • SPDEs with jumps.

  • Parameter estimation for SPDEs.

  • Numerical methods.

  • Backward Stochastic differential equations and SPDEs.

  • Large deviation results for SPDEs

  • Malliavin calculus for SPDEs.

  • Viscosity solutions for SPDEs.

  •           Etienne Pardoux: Stochastic partial differential equations, a review, Bull. Sc. Math.117, 29-47, 1993.



              Robert C Dalang:
               Extending the Martingale Measure Stochastic Integral with Applications to Spatially Homogeneous S.P.D.E.s"
                Electronic Journal of Probability, 1999.

               Istvan Gyöngy
    Existence and uniqueness results for semilinear stochastic partial differential equations
    Stochastic Processes and their Applications, 73 (2) (1998) pp. 271-299
    [Abstract][Full text]



               E Pardoux & D. Nualart: White noise driven quasilinear SPDEs with reflection, Prob. Theory and Rel. Fields 93, 77-89, 1992.

               Jan Ubøe and Tusheng Zhang
    A stability property of the stochastic heat equation
    Stochastic Processes and their Applications, 60 (2) (1995) pp. 247-260 [Abstract]



            Lorenzo Bertini, Giambattista Giacomin:
           On the long time behavior of the stochastic heat equation
            Probab Theory Relat Fields 114 (1999) 3, 279-289

            Elisa Alòs, Jorge A. León, David Nualart:
           Stochastic heat equation with random coefficients
            Probab Theory Relat Fields 115 (1999) 1, 41-94.

              Anna A. Kwiecioska
    Stabilization of partial differential equations by noise
    Stochastic Processes and their Applications, 79 (2) (1999) pp. 179-184 [Abstract][Full text]
    Annie Millet and Pierre-Luc Morien

    On a stochastic wave equation in two space dimensions: regularity of the solution and its density.
    Stochastic Processes and their Applications, 86 (1) (2000) pp. 141-162[Abstract][Full text]
               David Márquez-Carreras and Marta Sanz-Solé
    Small perturbations in a hyperbolic stochastic partial differential equation
    Stochastic Processes and their Applications, 68 (1) (1997) pp. 133-154
             Mueller, C. : Long time existence for the wave equation with a noise term.

            Ann. Probab. 25-1 (1997), 133-151. Math Review link.
    D. Nualart & S. Tindel: Quasilinear stochastic hyperbolic differential equations with nondecreasing coefficient. Potential analysis 7 (1997).
               David Nualart and Samy Tindel
    Quasilinear stochastic elliptic equations with reflection
    Stochastic Processes and their Applications, 57 (1) (1995) pp. 73-82 [Abstract]

              István Gyöngy and David Nualart
    Implicit scheme for quasi-linear parabolic partial differential equations perturbed by space-time white noise
    Stochastic Processes and their Applications, 58 (1) (1995) pp. 57-72 [Abstract]
    Hyek Yoo: Semi-discretization of stochastic partial differential equations on R by a finite-difference method , Mathematics of Computation, 69 (2000), 653-666..
    J.G. Gaines, Numerical experiments with S(P)DE's, in Stochastic Partial Differential Equations, A.M. Etheridge. ed., London Mathematical Society Lecture Note Series 216, Cambridge Univ. Press., 1995, pp. 55-71
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