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On the finiteness and tails of perpetuities under a Lamperti-Kiu map. (English) Zbl 1475.60085

Summary: Consider a Lamperti-Kiu Markov additive process \((J, \xi)\) on \(\{+, -\}\times\mathbb R\cup \{-\infty\}\), where \(J\) is the modulating Markov chain component. First we study the finiteness of the exponential functional and then consider its moments and tail asymptotics under Cramér’s condition. In the strong subexponential case we determine the subexponential tails of the exponential functional under some further assumptions.

MSC:

60G51 Processes with independent increments; Lévy processes
60G18 Self-similar stochastic processes
60J45 Probabilistic potential theory
91B70 Stochastic models in economics
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