On finiteness and tails of perpetuities under a Lamperti-Kiu MAP

Larbi Alili, David Woodford

Consider a Lamperti-Kiu Markov additive process $(J_t,{\xi }_t:t\ge 0)$ on $\{+,-\}\times \mathbb{R}\cup \infty$ where $J$ is the modulating Markov chain component. First, we study the fi…