Asymptotic stability of some stochastic evolution equations

摘要

Haussmann in [Journal of mathematical analysis and applications (1978)] discussed asymptotic stability in infinite dimension of the stochastic differential equationdX+AXdt=BXdWwhere A is a closed linear operator generating strongly continuous semigroup, B is a bounded operator, W is a Wiener process on a separable Hilbert space with covariance operator Z. Also Curtain [J. Math. Anal. Appl. (1981)] and others [Proceedings of the First Arabic Conference in Physics and Mathematics, Baghdad, 1978; Annals Prob. 24 (2) (1996); J. Math. Anal. Appl. (1978)] discussed the stability of a similar equations contains first and a second order derivatives. In this work we study the stability and solution of equation of the formdX+(A+Q)Xdt=BXdWwhere Q is a general closed linear operator.