PROBABILISTIC SOLUTIONS OF HIGH-ORDER PARTIAL-DIFFERENTIAL EQUATIONS

Blanchard P, HONGLER MO. PROBABILISTIC SOLUTIONS OF HIGH-ORDER PARTIAL-DIFFERENTIAL EQUATIONS. PHYSICS LETTERS A. 1993;180(3):225-231.We consider a stochastic differential equation in which the noise is the sum of a white noise, a Poisson noise and a continuous time Markov chain. The probability densities governing the dynamics solve high order partial differential equations and the solutions are expressible as convolutions of the densities characterizing the noise components. Relevant physical examples are presented