Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations

Published

Journal Article

We explore Itô stochastic differential equations where the drift term possibly depends on the infinite past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proven if the dependence on the past decays sufficiently fast. The results of this paper are then applied to stochastically forced dissipative partial differential equations such as the stochastic Navier-Stokes equation and stochastic Ginsburg-Landau equation. © World Scientific Publishing Company.

Full Text

Duke Authors

Cited Authors

  • Bakhtin, Y; Mattingly, JC

Published Date

  • October 1, 2005

Published In

Volume / Issue

  • 7 / 5

Start / End Page

  • 553 - 582

International Standard Serial Number (ISSN)

  • 0219-1997

Digital Object Identifier (DOI)

  • 10.1142/S0219199705001878

Citation Source

  • Scopus