Markov-modulated dependencies for a multiplicativeLindley-type recursion

In this paper, we study the stationary behaviour of a Markov-modulated multiplicative Lindley-type recursion W n+1 = [V n W n + Y n (V n )] + . Given the state of the background Markov chain, we consider two cases: a) V n equals either 1, or a ∈ (0, 1), or it is negative with certain probabilities, and Y n (V n ) := Y n = S n - A n+1 , where both A n and S n have a rational Laplace-Stieltjes transform (LST). b) V n equals 1 or -1 according to certain probabilities, and Y n (V n ) follows a more general scheme, dependent on V n . In both cases, we derive the LST of the stationary transform vector of W n n ∈ ℕ 0 . In the second case, we also provide a recursive approach to obtain the steady-state moments and provide an asymptotic result. A simple numerical example illustrates the theoretical findings.