Mean value theorems for stochastic integrals (Q1872190)

The paper deals with the approximation of stochastic integrals in the Itô sense with integrals of piecewise constant processes. Negative Sobolev spaces are used to estimate the rate of the approximation of the distribution of the stochastic integral. The research was motivated by problems of numerical approximations in control theory. The results are applied to Bellman equations with `non-constant' coefficients. The paper continues former research of the author on this subject [St. Petersbg. Math. J. 9, 639-650 (1998) and Algebra Anal. 9, 245-256 (1997; Zbl 0902.65035)].