Abstract
ABSTRACT In this paper we establish the existence of an invariant measure for a stochastic reaction–diffusion equation of the type , where f and σ are nonlinear maps and W is an infinite dimensional Q-–Wiener process. Our emphasis is on unbounded domain . Under a very mild dissipation assumption, we show the existence of a solution which is bounded in probability using a general Ito's formula. In addition, we investigate a type of equation for which bounded solutions may be obtained as a limit of an iteration scheme. Together with the compactness property of the heat equation semigroup, stochastic continuity and Feller property of the transition semigroup, the existence of such solution implies the existence of an invariant measure which is an important step in establishing the ergodic behaviour of the underlying physical system.
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