RANDOM EVOLUTIONS, MARKOV CHAINS, AND SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS

1 February 1969

journal article
Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences

Vol. 62 (2) , 305-308
https://doi.org/10.1073/pnas.62.2.305

Abstract

Several authors have considered Markov processes defined by the motion of a particle on a fixed line with a random velocity1, 6, 8, 10 or a random diffusivity.5, 12 A “random evolution” is a natural but apparently new generalization of this notion. In this note we hope to show that this concept leads to simple and powerful applications of probabilistic tools to initial-value problems of both parabolic and hyperbolic type. We obtain existence theorems, representation theorems, and asymptotic formulas, both old and new.

Keywords

BIOINFORMATICS
BIOMEDICAL RESEARCH
PARTIAL DIFFERENTIAL EQUATION
MARKOV PROCESS
MARKOV CHAIN
INITIAL VALUE PROBLEM

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