Stochastic process leading to wave equations in dimensions higher than one

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.

5 pages

Cited by in corpus (5)

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• Uniform Parametrization in Pseudo-Complex Hyperbolic Space
• Stochastic Representations for the Wave Equation on Graphs and their Scaling Limits