Stability of limit measures induced by stochastic differential equations on Hilbert space

AbstractIn this paper, we consider the questions of countable additivity of measures induced by stochastic differential equations on Hilbert space and also study the question of the existence of their asymptotic limits. We study the stability of these measures with respect to structural pertubations. In particular, we establish continuous dependence of these limit measures with respect to the generator of the semigroup, the initial measure, the initial covariance operator, the diffusion operator and combinations thereof. The author is not aware of any such studies conducted in the literature before