English

Stochastic solutions of the wave equation

Probability 2013-06-12 v1 Analysis of PDEs

Abstract

Unlike the heat equation or the Laplace equation, solutions of the wave equation on general domains have no known stochastic representation. This short note gives a simple solution to this well known problem in arbitrary dimensions. The proposed representation has several shortcomings, one of which is that it does not cover all solutions. Still, it is proof that a large class of nontrivial solutions of the wave equation in general dimensions and domains may indeed be represented stochastically.

Keywords

Cite

@article{arxiv.1306.2382,
  title  = {Stochastic solutions of the wave equation},
  author = {Sourav Chatterjee},
  journal= {arXiv preprint arXiv:1306.2382},
  year   = {2013}
}

Comments

6 pages

R2 v1 2026-06-22T00:31:41.849Z