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...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2006
- Institución:
- Universidad del Rosario
- Repositorio:
- Repositorio EdocUR - U. Rosario
- Idioma:
- eng
- OAI Identifier:
- oai:repository.urosario.edu.co:10336/14385
- Acceso en línea:
- http://repository.urosario.edu.co/handle/10336/14385
- Palabra clave:
- Branching random motion
Travelling wave
Feynman-Kac connection
Non-linear hyperbolic system
Mckean solution
- Rights
- License
- Abierto (Texto Completo)
| Summary: | 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. |
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