Branching random motions, nonlinear hyperbolic systems and travellind waves

Nikita Ratanov

ESAIM: Probability and Statistics (2006)

  • Volume: 10, page 236-257
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Ratanov, Nikita. "Branching random motions, nonlinear hyperbolic systems and travellind waves." ESAIM: Probability and Statistics 10 (2006): 236-257. <http://eudml.org/doc/249754>.

@article{Ratanov2006,
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. },
author = {Ratanov, Nikita},
journal = {ESAIM: Probability and Statistics},
keywords = {Branching random motion; travelling wave; Feynman-Kac connection; non-linear hyperbolic system; McKean solution.; branching random motion; McKean solution; Kolmogorov type backward equation; Kolmogorov-Petrovskii-Piskunov equation},
language = {eng},
month = {5},
pages = {236-257},
publisher = {EDP Sciences},
title = {Branching random motions, nonlinear hyperbolic systems and travellind waves},
url = {http://eudml.org/doc/249754},
volume = {10},
year = {2006},
}

TY - JOUR
AU - Ratanov, Nikita
TI - Branching random motions, nonlinear hyperbolic systems and travellind waves
JO - ESAIM: Probability and Statistics
DA - 2006/5//
PB - EDP Sciences
VL - 10
SP - 236
EP - 257
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.
LA - eng
KW - Branching random motion; travelling wave; Feynman-Kac connection; non-linear hyperbolic system; McKean solution.; branching random motion; McKean solution; Kolmogorov type backward equation; Kolmogorov-Petrovskii-Piskunov equation
UR - http://eudml.org/doc/249754
ER -

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