ON NONLINEAR EQUATIONS RELATED TO THE DISTRIBUTIONS OFCOMPOSITION OF PROCESSES

The relationship between non-trivial linear partial differential equations and the probabilitydensities of compositions of relevant processes has been pointed out in the recent literature.In this note, we construct exact solutions for nonlinear partial differential equations startingfrom these linear equations by using simple transformations. In this way, we have an interestingbridge between the fundamental solutions of linear equations with a clear probabilistic meaningand the construction of exact interesting solutions for the corresponding nonlinear equations.This method can be obviously generalized to many other cases.