Branching random motions, nonlinear hyperbolic systems and traveling waves

Nikita Ratanov ()

No 4331, Borradores de Investigación from Universidad del Rosario

Abstract: 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.

Keywords: non-linear hyperbolic system; branching random motion; traveling wave; Feynman-Kac connection; McKean solution (search for similar items in EconPapers)
Pages: 32
Date: 2004-07-02
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:col:000091:004331

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