Branching random motions, nonlinear hyperbolic systems and travelling waves

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 (Kolmog...

Descripción completa

Detalles Bibliográficos
Autor Principal: Ratanov, Nikita
Otros Autores: Facultad de Economía
Formato: Artículo (Article)
Lenguaje:Inglés (English)
Publicado: 2006
Materias:
Acceso en línea:http://repository.urosario.edu.co/handle/10336/14385
Descripción
Sumario: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.