## 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 language | English (US) |
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Pages (from-to) | 236-257 |

Number of pages | 22 |

Journal | ESAIM - Probability and Statistics |

Volume | 10 |

DOIs | |

State | Published - 2006 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability