Recursive estimators with Markovian jumps

Recursive stochastic algorithms have various applications. In the literature, it is assumed that the true value lies in a connected domain. But, in many cases, it is known that the true value is contained in the union of a finite number of pairwise disjoint sets instead of a connected domain. In these situations, the existing algorithms may be not applicable. To cope with this problem, this paper proposes recursive stochastic algorithms with (event-triggered) Markovian jumps and presents sufficient conditions for almost sure convergence of the proposed algorithms. As an example of applications, this paper significantly improves an existing adaptive algorithm with the proposed method for consistent estimation of non-minimum phase zeros.