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

$$du\left( t \right) = a\left( t \right)\left[ {C\left( {u\left( t \right),x\left( t \right)} \right)dt + \sigma \left( {u\left( t \right)} \right)dw\left( t \right)} \right]$$

in a random semi-Markov medium described by an ergodic semi-Markov process x(t).