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The distribution of random motion in semi-Markov media
A. Pogorui Zhytomyr Ivan Franko State University
Abstract:
This paper deals with the random motion with finite speed along uniformly distributed directions, where the direction alternations occur according to renewal epochs of a general distribution. We derive a renewal equation for the characteristic function of a transition density of multidimensional motion. By using the renewal equation, we study the behavior of the transition density near the sphere of its singularity in two- and three-dimensional cases. For $\left(n-1\right)$-Erlang distributed steps of the motion in an $n$-dimensional space ($n\geq 2$), we have obtained the characteristic function as a solution of the renewal equation. As an example, we have derived the distribution for the three-dimensional random motion.
Keywords:
Random motion, characteristic function, convolution, Fourier transform, Laplace transform, Dirac delta-function.
Citation:
A. Pogorui, “The distribution of random motion in semi-Markov media”, Theory Stoch. Process., 18(34):1 (2012), 111–118
Linking options:
https://www.mathnet.ru/eng/thsp22 https://www.mathnet.ru/eng/thsp/v18/i1/p111
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Abstract page: | 93 | Full-text PDF : | 31 | References: | 22 |
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