Singularly perturbed telegraph equations with applications in the random walk theory. (English) Zbl 0909.35011

Banasiak, Jacek; Mika, Janusz R.

J. Appl. Math. Stochastic Anal. 11, No. 1, 9-28 (1998).

Summary: We analyze singularly perturbed telegraph systems applying the newly developed compressed asymptotic method and show that the diffusion equation is an asymptotic limit of a 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.

MSC:

35B25	Singular perturbations in context of PDEs
60G50	Sums of independent random variables; random walks
35L50	Initial-boundary value problems for first-order hyperbolic systems

Keywords:

diffusion approximation; compressed asymptotic method