Mean value theorems for stochastic integrals. (English) Zbl 1021.60042

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)].


60H05 Stochastic integrals
93E20 Optimal stochastic control
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs


Zbl 0902.65035
Full Text: DOI


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