Local asymptotics of a Markov modulated random walk with heavy-tailed increments |
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| Authors: | Bing Chang Wang Yuan Yuan Liu |
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| Affiliation: | (1) Department of Actuarial Mathematics, Heriot-Watt University, Riccarton, Edinburgh, UK;(2) Sobolev Institute of Mathematics, Novosibirsk, Russia;(3) Sobolev Institute of Mathematics of the Russian Academy of Sciences, 4 Koptyuga pr., 630090 Novosibirsk, Russia |
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| Abstract: | In this paper, we obtain sufficient and necessary conditions for local asymptotics for the maximum of a Markov modulated random walk with long-tailed increments and negative drifts, where the local asymptotics means asymptotic behaviour of P(· ∈ (x, x + z]) for each z > 0, as x→∞. Our results extend and improve the existing ones in the literature. |
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| Keywords: | Mavkov modulated random walk local asymptotics long-tailed distributions subexpo- nential distributions Wiener-Hopf factorization |
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