Branching random motions, nonlinear hyperbolic systems and travelling waves

Nikita Ratanov

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)236-257
Number of pages22
JournalESAIM - Probability and Statistics
Volume10
DOIs
StatePublished - 2006

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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