Branching random motions, nonlinear hyperbolic systems and travelling waves

Resultado de la investigación: Contribución a RevistaArtículo

3 Citas (Scopus)

Resumen

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.
Idioma originalEnglish (US)
Páginas (desde-hasta)236-257
Número de páginas22
PublicaciónESAIM - Probability and Statistics
DOI
EstadoPublished - dic 1 2006

Huella dactilar

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

Citar esto

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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. {\circledC} EDP Sciences, SMAI 2006.",
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Branching random motions, nonlinear hyperbolic systems and travelling waves. / Ratanov, Nikita.

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

Resultado de la investigación: Contribución a RevistaArtículo

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.

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M3 - Article

SP - 236

EP - 257

JO - ESAIM - Probability and Statistics

JF - ESAIM - Probability and Statistics

SN - 1292-8100

ER -