Stochastic solutions of the wave equation

Understand

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.