Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance

T. Khaniyev, T. Kesemen, R. Aliyev and A. Kokangul

Statistics & Probability Letters, 2008, vol. 78, issue 6, 785-793

Abstract: In this paper, a semi-Markovian random walk process (X(t)) with a discrete interference of chance is constructed and the ergodicity of this process is discussed. Some exact formulas for the first- and second-order moments of the ergodic distribution of the process X(t) are obtained, when the random variable [zeta]1 has an exponential distribution with the parameter [lambda]>0. Here [zeta]1 expresses the quantity of a discrete interference of chance. Based on these results, the third-order asymptotic expansions for mathematical expectation and variance of the ergodic distribution of the process X(t) are derived, when [lambda]-->0.

Keywords: Random; walk; First; jump; Ergodic; distribution; Asymptotic; expansion; Ladder; variable; Discrete; interference; of; chance (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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