| Issue |
ESAIM: PS
Volume 10, September 2006
|
|
|---|---|---|
| Page(s) | 236 - 257 | |
| DOI | https://doi.org/10.1051/ps:2006009 | |
| Published online | 03 May 2006 | |
Branching random motions, nonlinear hyperbolic systems and travellind waves
Faculty of Economics, Rosario University,
Cl. 14, No. 4-69, Bogotá, Colombia;
nratanov@urosario.edu.co
Received:
25
April
2005
Revised:
20
August
2005
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.
Mathematics Subject Classification: 35L60 / 60J25 / 60J80 / 60J85
Key words: Branching random motion / travelling wave / Feynman-Kac connection / non-linear hyperbolic system / McKean solution.
© EDP Sciences, SMAI, 2006
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.