Branching random motions, nonlinear hyperbolic systems and traveling waves

A branching random motion on a line, with abrupt changes of direction, is studied. The branching mechanism, being independient of random motion, and intensities of reverses are defined by a particle's current direction. A soluton of a certain hyperbolic system of coupled non-linear equations (Kolmogorov type backward equation) have a so-called McKean representation via such processes. Commonly this system possesses traveling-wave solutions. The convergence of solutions with Heaviside terminal data to the travelling waves is discussed.This Paper realizes the McKean programme for the Kolmogorov-Petrovskii-Piskunov equation in this case. The Feynman-Kac formula plays a key role.

• Fecha de publicación: 2004
• Institución: Universidad del Rosario
• Repositorio: Repositorio EdocUR - U. Rosario
• Idioma: eng
• OAI Identifier: oai:repository.urosario.edu.co:10336/11126
• Acceso en línea: https://doi.org/10.48713/10336_11126; http://repository.urosario.edu.co/handle/10336/11126
• Palabra clave: Análisis; Non-linear hyperbolic system; Branching random motion; Feynman-Kac connection; McKean solution; Traveling wave; Ecuaciones diferenciales; Ecuaciones diferenciales hiperbólicas; Procesos de bifurcación; Tubos de ondas progresivas; Matemáticas financieras
• License: http://purl.org/coar/access_right/c_abf2