Abstract. The asymptotic behavior of the modified discrete stochastic optimization procedure (SOP) in the Markov environment in the averaging scheme is investigated. Additional SOP optimization parameters are introduced and are used to obtain different behavior of fluctuations on increasing time intervals. The normalization-dependent form of boundary generator is established and it is shown that for certain values of the input parameters the modified discrete SOP is asymptotically normal.

Keywords: Markov process, stochastic optimization, asymptotic behavior, averaging scheme.