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Investigation of some probabilistic characteristics of one class of semi-Markov wandering with delaying screens

Investigation of some probabilistic characteristics of one class of semi-Markov wandering with... The process of semi-Markov wandering with delaying screens “b” and “a” (a > b > 0) is constructed by the given sequence of independent and identically distributed random vectors (ξ i , η i ), i ≥ 1. The integral equation for the Laplace transform by time and the Laplace-Stieltjes transform by the phase of its conditional distribution is derived. If the wandering occurs by a complicated Laplace distribution, the ergodic distribution of the process and its moments are found. Then, the integral equation for the generating function of the conditional distribution of the number of process steps at which it firstly reaches the level a is derived. When the wandering occurs by the simple Laplace distribution, its generating functions and moments are found. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automatic Control and Computer Sciences Springer Journals

Investigation of some probabilistic characteristics of one class of semi-Markov wandering with delaying screens

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Publisher
Springer Journals
Copyright
Copyright © 2014 by Allerton Press, Inc.
Subject
Computer Science; Control Structures and Microprogramming
ISSN
0146-4116
eISSN
1558-108X
DOI
10.3103/S0146411614020059
Publisher site
See Article on Publisher Site

Abstract

The process of semi-Markov wandering with delaying screens “b” and “a” (a > b > 0) is constructed by the given sequence of independent and identically distributed random vectors (ξ i , η i ), i ≥ 1. The integral equation for the Laplace transform by time and the Laplace-Stieltjes transform by the phase of its conditional distribution is derived. If the wandering occurs by a complicated Laplace distribution, the ergodic distribution of the process and its moments are found. Then, the integral equation for the generating function of the conditional distribution of the number of process steps at which it firstly reaches the level a is derived. When the wandering occurs by the simple Laplace distribution, its generating functions and moments are found.

Journal

Automatic Control and Computer Sciences – Springer Journals

Published: May 10, 2014

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