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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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 -