Approximate continuity of certain functionals on Wiener space
This paper was initiated through the support theorem obtained by Stroock and Varadhan concerning the solutions of stochastic differential equations with bounded coefficients. Their result can be seen as a property of regularity which we call here approximate continuity. We are mainly concerned with definitions closely related to the original idea of Stroock and Varadhan by introducing an approximate Lipschitz property and by studying the approximate continuity in \(L^p\). We show that functionals defined with stochastic differential equations or like infinite sums of particular processes possess some of these properties. Furthermore, we estimate the rate of convergence associated with these notions.
scientific article; zbMATH DE number 891035