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arXiv · 1001.3821

Stochastic process leading to wave equations in dimensions higher than one

A. V. Plyukhin
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Abstract

Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles with constant speed and transitions between discreet allowed velocity directions. A new ingredient is that transitions into a given velocity state depend on spatial derivatives of other states populations, rather than on populations themselves. This feature requires the sacrifice of the single-particle character of the model, but allows to imitate the Huygens' principle and to recover wave equations in arbitrary dimensions.

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BibTeXRIS

A. V. Plyukhin. 2010-01-21. Stochastic process leading to wave equations in dimensions higher than one. https://doi.org/10.1103/physreve.81.021113

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