An asymptotic expansion for the distribution of the supremum of a Markov-modulated random walk
Mikhail Sgibnev
Source: Tsukuba J. Math. Volume 35, Number 1
(2011), 103-113.
Abstract
We obtain an asymptotic expansion for the distribution of the supremum of a Markov-modulated random walk, which takes into account the influence of the roots of the characteristic equation. An estimate is given for the remainder term by means of submultiplicative weight functions.
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Keywords: Supremum; Markov-modulated random walk; Finite Markov chain; Submultiplicative function; Characteristic equation; Asymptotic expansion; Banach algebra
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Tsukuba Journal of Mathematics
