An introduction to stochastic partial differential equations

  • John B. Walsh
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1180)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Aldous, D., Stopping times and tightness, Ann. Prob. 6 (1978), 335–340.MATHMathSciNetGoogle Scholar
  2. [2]
    Bakry, D., Semi martingales à deux indices, Sem. de Prob. XV, Lecture Notes in Math 850, 671–672.Google Scholar
  3. [3]
    Balakrishnan, A. V., Stochastic bilinear partial differential equations, in Variable Structure Systems, Lecture Notes in Economics and Mathematical Systems 3, Springer Verlag, 1975.Google Scholar
  4. [4]
    Bensoussan, A. and Temam, R., Equations stochastiques du type Navier-Stokes, J. Fcl. Anal. 13 (1973), 195–222.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Billingsley, P., Convergence of Probability Measures, Wiley, New York, 1968.MATHGoogle Scholar
  6. [6]
    Brennan, M. D., Planar semimartingales, J. Mult. Anal. 9 (1979), 465–486.MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Burkholder, D. L., Distribution function inequalities for martingales, Ann. Prob. 1 (1973), 19–42.MATHMathSciNetGoogle Scholar
  8. [8]
    Cabaña, E., On barrier problems for the vibrating string, ZW 22 (1972), 13–24.MATHGoogle Scholar
  9. [9]
    Cairoli, R., Sur une equation differentielle stochastique, C.R. 274 (1972), 1738–1742.MathSciNetGoogle Scholar
  10. [10]
    Cairoli, R. and Walsh, J. B., Stochastic integrals in the plane, Acta Math 134 (1975), 111–183.MATHMathSciNetCrossRefGoogle Scholar
  11. [11]
    Curtain, R. F. and Falb, P. L., Stochastic differential equations in Hilbert spaces, J. Diff. Eq. 10 (1971), 434–448.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Da Prato, G., Regularity results of a convolution stochastic integral and applications to parabolic stochastic equations in a Hilbert space (Preprint).Google Scholar
  13. [13]
    Dawson, D., Stochastic evolution equations and related measure processes, J. Mult. Anal. 5 (1975), 1–52.MATHCrossRefGoogle Scholar
  14. [14]
    Dawson, D., Stochastic evolution equations, Math Biosciences 15, 287–316.Google Scholar
  15. [15]
    Dawson, D. and Hochberg, K. J., The carrying dimension of a stochastic measure diffusion. Ann. Prob. 7 (1979).Google Scholar
  16. [16]
    Dynkin, E. B., Gaussian and non-Gaussian random fields associated with Markov processes, J. Fcl. Anal. 55 (1984), 344–376.MATHMathSciNetCrossRefGoogle Scholar
  17. [17]
    Dynkin, E. B. and Mandelbaum A., Symmetric statistics, Poisson point processes, and multiple Wiener integrals, Ann. Math. Stat 11 (1983), 739–745.MATHMathSciNetGoogle Scholar
  18. [18]
    Evstigneev, I. V., Markov times for random fields, Theor. Prob. Appl. 22 (1978), 563–569.CrossRefGoogle Scholar
  19. [19]
    Faris, W. G., and Jona-Lasinio, G., Large fluctuations for a nonlinear heat equation with white noise, J. Phys. A: Math, Gen. 15 (1982), 3025–3055.MATHMathSciNetCrossRefGoogle Scholar
  20. [20]
    Fleming, W. and Viot, M., Some measure-valued Markov processes in population genetics theory, Indiana Univ. Journal 28 (1979), 817–843.MATHMathSciNetCrossRefGoogle Scholar
  21. [21]
    Fouque, J-P., La convergence en loi pour les processus à valeurs dans un éspace nucleaire, Ann. IHP 20 (1984), 225–245.MATHMathSciNetGoogle Scholar
  22. [22]
    Garsia, A., Continuity properties of Gaussian processes with multidimensional time parameter, Proc. 6th Berkeley Symposium, V.II, 369–374.Google Scholar
  23. [23]
    Garsia, A., Rodemich, G., and Rumsey, H. Jr., A real variable lemma and the continuity of paths of some Gaussian processes, Indiana U. Math. J. 20 (1970), 565–578.MATHMathSciNetCrossRefGoogle Scholar
  24. [24]
    Gelfand, I. M. and Vilenkin, N. Ya., Generalized Functions, V.4, Academic Press, New York-London 1964.Google Scholar
  25. [25]
    Gihman, I. I., and Skorohod, A. V., The Theory of Stochastic Processes, III, Springer-Verlag Berlin (1979).MATHGoogle Scholar
  26. [26]
    Gorostitza, L., High density limit theorems for infinite systems of unscaled branching Brownian motions, Ann. Prob. 11 (1983), 374–392; Correction, Ann. Prob. 12 (1984), 926–927.Google Scholar
  27. [27]
    Greiner, P., An asymptotic expansion for the heat equation, Arch. Ratl. Mech. Anal. 41 (1971), 163–218.MATHMathSciNetCrossRefGoogle Scholar
  28. [28]
    Harris, T. E., The Theory of Branching Processes, Prentice-Hall, Englewood Cliffs, N.J., 1963.MATHGoogle Scholar
  29. [29]
    Holley, R. and Stoock, D., Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions, Publ. RIMS Kyoto Univ. 14 (1978), 741–788.MATHCrossRefGoogle Scholar
  30. [30]
    Hormander, L. Linear Partial Differential Operators, Springer Verlag, Berlin, Heidelberg, New York, 1963.Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • John B. Walsh

There are no affiliations available

Personalised recommendations