Publications [#43490] of Jonathan C. Mattingly

Papers Published

1. 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.)
   (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.