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Invariant measures for semilinear stochastic equations. (English) Zbl 0758.60057
The stochastic evolution \(dX=(AX+F(X))dt+B(X)dW(t)\) in a Hilbert space is considered, where \(A\) is the infinitesimal generator of a \(C_ 0\)- semigroup \(S(t)\), \(t\geq 0\), \(F\) and \(B\) are linear or nonlinear mappings, and \(W(\cdot)\) is a Wiener process. The existence and uniqueness of invariant measures are proved for dissipative equations and linear stable equations, while the existence is proved for equations with compact \(S(\cdot)\).

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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