The Annals of Probability

On SPDE's and superdiffusions

N. V. Krylov

Full-text: Open access

Abstract

Several stochastic partial differential equations are derived for multidimensional superdiffusions.

Article information

Source
Ann. Probab., Volume 25, Number 4 (1997), 1789-1809.

Dates
First available in Project Euclid: 7 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1023481111

Digital Object Identifier
doi:10.1214/aop/1023481111

Mathematical Reviews number (MathSciNet)
MR1487436

Zentralblatt MATH identifier
0904.60047

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15]

Keywords
Stochastic partial differential equations superdiffusions

Citation

Krylov, N. V. On SPDE's and superdiffusions. Ann. Probab. 25 (1997), no. 4, 1789--1809. doi:10.1214/aop/1023481111. https://projecteuclid.org/euclid.aop/1023481111


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References

  • [1] Aleksandrov, A. D. (1958). Dirichlet's problem for the equation Det zij = z1 zn z x1 xn. Vestnik Leningrad Univ. 13 5-24. (In Russian.)
  • [2] Cheng, S. Y. and Yau, S. T. (1977). On the regularity of the Monge-Amp ere equation det 2u/ xi xj = F x u. Comm. Pure Appl. Math. 30 41-68.
  • [3] Dawson, D. A. (1993). Measure-valued Markov processes. ´Ecole d' ´Et´e de Probabilit´es de Saint Flour. Lecture Notes in Math. 1541 1-292. Springer, Berlin.
  • [4] Dynkin, E. B. (1993). Superprocesses and partial differential equations. Ann. Probab. 21 1185-1262.
  • [5] Dynkin, E. B., Kuznetsov, S. E. and Skorohod, A. V. (1996). Branching measure-valued processes. Preprint.
  • [6] Gy ¨ongy, I. and Krylov, N. V. (1980). On stochastic equations with respect to semimartingales I. Stochastics 4 1-21.
  • [7] Konno, N. and Shiga, T. (1988). Stochastic partial differential equations for some measurevalued diffusions. Probab. Theory Related Fields 79 201-225.
  • [8] Krasnoselskii, M. A., Pustylnik, E. I., Sobolevski, P. E. and Zabrejko, P. P. (1966). Integral Operators in Spaces of Summable Functions. Nauka, Moscow. (In Russian. English trans.: (1976) Noordhoff, Leyden.)
  • [9] Krylov, N. V. (1995). Introduction to the Theory of Diffusion Processes. Amer. Math. Soc., Providence, RI.
  • [10] Krylov, N. V. (1996). On Lp-theory of stochastic partial differential equations. SIAM J. Math. Anal. 27 313-340.
  • [11] Reimers, M. (1989). One-dimensional stochastic partial differential equations and the branching measure diffusion. Probab. Theory Related Fields 81 319-340.