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Branching random motions,nonlinear hyperbolic systems and travellind waves

Published online by Cambridge University Press:  03 May 2006

Nikita Ratanov
Nikita Ratanov*
Affiliation:
Faculty of Economics, Rosario University, Cl. 14, No. 4-69, Bogotá, Colombia; nratanov@urosario.edu.co
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Abstract

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independent of random motion, and intensities of reverses are defined by a particle's current direction. A solution of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) has a so-called McKean representation via such processes. Commonly this system possesses travelling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed. The paper realizes the McKean's program for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.

Keywords

Branching random motiontravelling waveFeynman-Kac connectionnon-linear hyperbolic systemMcKean solution.

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 10 , February 2006, pp. 236 - 257
Copyright
© EDP Sciences, SMAI, 2006

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