Math @ Duke

Publications [#243860] of Jonathan C. Mattingly
Papers Published
 Bakhtin, Y; Mattingly, JC, Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations,
Communications in Contemporary Mathematics, vol. 7 no. 5
(2005),
pp. 553582, World Scientific, ISSN 02191997 (ISSN: 02191997.) [MR2175090], [math.PR/0509166], [doi]
(last updated on 2017/12/13)
Abstract: 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 NavierStokes equation and stochastic GinsburgLandau equation. © World Scientific Publishing Company.


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