Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 1, Pages 9-28

Singularly perturbed telegraph equations with applications in the random walk theory

Jacek Banasiak1 and Janusz R. Mika1,2,3

1University of Natal, Dept. of Mathematics and Applied Mathematics, Private Bag XI0, Dalbridge 4014, Durban, South Africa
2Institute of Atomic Energy, Świerk, Otwock 05-400, Poland
3Institute of Mathematics, Technical University of Lódź, Poland

Received 1 March 1996; Revised 1 May 1997

Copyright © 1998 Jacek Banasiak and Janusz R. Mika. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the paper we analyze singularly perturbed telegraph systems applying the newly developed compressed asymptotic method and show that the diffusion equation is an asymptotic limit of singularly perturbed telegraph system of equations. The results are applied to the random walk theory for which the relationship between correlated and uncorrelated random walks is explained in asymptotic terms.