Abstract
In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.
Similar content being viewed by others
References
Ma Zhiming, Xiang Kainan. Superprocesses of stochastic flows, Ann Probab,2001, 29: 317–343.
Chow P L. Function space differential equations associated with a stochastic partial differential equation, Indiana Univ Math J, 1976, 25: 609–627.
Dawson D A. Infinitely divisible random measure and superprocesses, Silivri, Turkey,1992.
Dawson D A. Measure-valued Markov Process, Berlin: Springer-Verlag, 1993,1541: 1–260.
Dawson D A, Li Z H, Wang H. Superprocess with dependent spatial motion and general branching densities, Elect J Probab,2001, 6: Paper 25.
Dawson D A, Vaillancourt J. Stochastic Mckean-Vlasov equations, Nonlinear Diff Eq Appl,1995, 2: 199–229.
Dynkin E B. An Introduction to Branching Measure-valued Processes, Amer Math Soc, Providence, RI,1994.
Darlinrg RWR. Rate of growth of the coalescent set in a coalescing stochastic flow, Stochastics, 1988, 23: 465–580.
Kotelenez P. A class quasilinear stochastic partial differential equations of Mckean-Vlasov type with mass conservation, Probab Theory Related Fields, 1995, 102: 159–188.
Le Gall J F. A class path-valued Markov processes and its applications to superprocesses, Probab Theory Related Fields, 1993, 95: 25–46.
Wang H. A class of measure-valued branching diffusions in a random medium, Stochastic Analysis and Applications, 1998, 16: 753–786.
Mytnik L. Superprocesses in random environments, Ann Probab, 1996, 24: 1953–1978.
Ethier S N, Kurts T G. Markov Processes:Characterization and convergence, New York: Wiley, 1986.
Author information
Authors and Affiliations
Additional information
Supported by the Natural Science Foundation of Henan Province (2004601018).
Rights and permissions
About this article
Cite this article
Zhao, Q., Yan, G. Stochastic flows of mappings. Appl. Math. Chin. Univ. 22, 343–352 (2007). https://doi.org/10.1007/s11766-007-0312-4
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11766-007-0312-4