On the semi-Markovian random walk with two reflecting barriers

In this paper, the semi-Markovian random walk with two reflecting barriers is constructed mathematically and non-stationary distribution functions of it are expressed by means of the probability characteristics of renewal process {T n } and random walk {Y n } without barriers. In particular, when th...

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Bibliographic Details
Published in:Stochastic analysis and applications 2001-10, Vol.19 (5), p.799-819
Main Authors: Khanıev, Tahır A., Unver, İhsan, Maden, Selahattın
Format: Article
Language:English
Subjects:
Exact sciences and technology
Inference from stochastic processes
time series analysis
Markov processes
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
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Summary:In this paper, the semi-Markovian random walk with two reflecting barriers is constructed mathematically and non-stationary distribution functions of it are expressed by means of the probability characteristics of renewal process {T n } and random walk {Y n } without barriers. In particular, when the time between two jump instants has exponential or Erlang distribution, explicit formulae are obtained for non-stationary distribution functions of the process. Moreover, explicit expressions are given for expected value, variance and moment generating function of the first reflection moment, an important boundary functional, of the process from lower reflecting barrier.
ISSN:0736-2994
1532-9356
DOI:10.1081/SAP-120000222