### Abstract

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

Number of pages | 22 |

Journal | ESAIM - Probability and Statistics |

DOIs | |

State | Published - Dec 1 2006 |

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*ESAIM - Probability and Statistics*, pp. 236-257. https://doi.org/10.1051/ps:2006009

**Branching random motions, nonlinear hyperbolic systems and travelling waves.** / Ratanov, Nikita.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Branching random motions, nonlinear hyperbolic systems and travelling waves

AU - Ratanov, Nikita

PY - 2006/12/1

Y1 - 2006/12/1

N2 - 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. © EDP Sciences, SMAI 2006.

AB - 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. © EDP Sciences, SMAI 2006.

U2 - 10.1051/ps:2006009

DO - 10.1051/ps:2006009

M3 - Article

SP - 236

EP - 257

JO - ESAIM - Probability and Statistics

JF - ESAIM - Probability and Statistics

SN - 1292-8100

ER -