Continuous procedure of stochastic approximation in a semi-Markov medium
Abstract
Using the Lyapunov function for an averaged system, we establish conditions for the convergence of the procedure of stochastic approximation $$du(t)=a(t)[C(u(t),x(t))dt+σ(u(t))dw(t)]$$ in a random semi-Markov medium described by an ergodic semi-Markov process $x(t)$.
English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 5, pp 862–872.
Citation Example: Chabanyuk Ya. M. Continuous procedure of stochastic approximation in a semi-Markov medium // Ukr. Mat. Zh. - 2004. - 56, № 5. - pp. 713–720.
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