Branching random motions, nonlinear hyperbolic systems and travelling waves

Nikita Ratanov

Research output: Contribution to journal › Article

3 Citations (Scopus)

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. © EDP Sciences, SMAI 2006.
Original languageEnglish (US)
Pages (from-to)236-257
Number of pages22
JournalESAIM - Probability and Statistics
DOIs
StatePublished - Dec 1 2006

Fingerprint

Nonlinear Hyperbolic Systems
Traveling Wave
Branching
Oliver Heaviside
Feynman-Kac Formula
Convergence of Solutions
Motion
Hyperbolic Systems
Traveling Wave Solutions
Reverse
Nonlinear Equations
Line

Cite this

Ratanov, Nikita. / Branching random motions, nonlinear hyperbolic systems and travelling waves. In: ESAIM - Probability and Statistics. 2006 ; pp. 236-257.
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Ratanov, N 2006, 'Branching random motions, nonlinear hyperbolic systems and travelling waves', 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.

In: ESAIM - Probability and Statistics, 01.12.2006, p. 236-257.

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 -

Ratanov N. Branching random motions, nonlinear hyperbolic systems and travelling waves. ESAIM - Probability and Statistics. 2006 Dec 1;236-257. https://doi.org/10.1051/ps:2006009

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