Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance

ALIYEV R., KÜÇÜK Z., Khaniyev T.

APPLIED MATHEMATICAL MODELLING, vol.34, no.11, pp.3599-3607, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 11
  • Publication Date: 2010
  • Doi Number: 10.1016/j.apm.2010.03.009
  • Journal Name: APPLIED MATHEMATICAL MODELLING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3599-3607
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this study, a semi-Markovian random walk with a discrete interference of chance (X(t)) is considered and under some weak assumptions the ergodicity of this process is discussed. The exact formulas for the first four moments of ergodic distribution of the process X(t) are obtained when the random variable which is describing a discrete interference of chance, has a triangular distribution in the interval Is, SI with center (S + s)/2. Based on these results, the asymptotic expansions with three-term are obtained for the first four moments of the ergodic distribution of X(t), as a (S - s)/2 -> infinity. Furthermore, the asymptotic expansions for the variance, skewness and kurtosis of the ergodic distribution of the process X(t) are established. Finally, by using Monte Carlo experiments it is shown that the given approximating formulas provide high accuracy even for small values of parameter a. (c) 2010 Elsevier Inc. All rights reserved.