Publications [#43490] of Jonathan C. Mattingly
Papers Published
- Bakhtin, Yuri and Mattingly, Jonathan C., Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations,
Communications in Contemporary Mathematics, vol. 7 no. 5
(2005),
pp. 553--582, World Scientific (ISSN: 0219-1997.) [MR2175090], [math.PR/0509166]
(last updated on 2006/01/09)Abstract:
We explore ItÆo stochastic di erential equations where the drift term has possibly infinite dependence on the past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coe cients. Uniqueness of the stationary solution is proved if the dependence on the past decays su - ciently fast. The results of this paper are then applied to stochastically forced dissipative partial di erential equations such as the stochastic Navier-Stokes equation and stochastic Ginsburg-Landau equation.