# Branching random motions, nonlinear hyperbolic systems and travellind waves

ESAIM: Probability and Statistics (2006)

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

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topRatanov, 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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