Borkar, Vivek; Gaitsgory, Vladimir Averaging of singularly perturbed controlled stochastic differential equations. (English) Zbl 1139.93022 Appl. Math. Optimization 56, No. 2, 169-209 (2007). From the authors abstract: “An averaged system to approximate the slow dynamics of a two timescale nonlinear stochastic control system is introduced. Validity of the approximation is established. Special cases are considered to illustrate the general theory.” The controlled system of stochastic differential equations is driven by multidimensional, independent Wiener processes. Reviewer: Henri Schurz (Carbondale) Cited in 21 Documents MSC: 93C70 Time-scale analysis and singular perturbations in control/observation systems 34C29 Averaging method for ordinary differential equations 34E15 Singular perturbations for ordinary differential equations 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 93E03 Stochastic systems in control theory (general) Keywords:singularly perturbed stochastic differential equations; controlled systems; averaging; occupational measures; limit occupational measures sets; approximation of slow motions PDFBibTeX XMLCite \textit{V. Borkar} and \textit{V. Gaitsgory}, Appl. Math. Optim. 56, No. 2, 169--209 (2007; Zbl 1139.93022) Full Text: DOI