The Annals of Probability

On Diffusion Processes and Their Semigroups in Hilbert Spaces with an Application to Interacting Stochastic Systems

G. Leha and G. Ritter

Full-text: Open access

Abstract

We study solutions to stochastic differential equations in Hilbert space. In particular we give sufficient conditions for nonexplosion and for the associated semigroup to be of Feller type. We also give applications to systems of stochastic differential equations.

Article information

Source
Ann. Probab., Volume 12, Number 4 (1984), 1077-1112.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993143

Digital Object Identifier
doi:10.1214/aop/1176993143

Mathematical Reviews number (MathSciNet)
MR757771

Zentralblatt MATH identifier
0546.60082

JSTOR
links.jstor.org

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H20: Stochastic integral equations 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Stochastic differential equation in Hilbert space interacting stochastic system interacting process diffusion process nonexplosion Feller semigroup

Citation

Leha, G.; Ritter, G. On Diffusion Processes and Their Semigroups in Hilbert Spaces with an Application to Interacting Stochastic Systems. Ann. Probab. 12 (1984), no. 4, 1077--1112. doi:10.1214/aop/1176993143. https://projecteuclid.org/euclid.aop/1176993143


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