Convolutions with probability densities and applications to PDEs

Abstract

In this article we introduce several new convolution operators, generated by some known probability densities. By using the inverse Fourier transform and taking inverse steps (in the analogues of the classical procedures used for example in the heat or Laplace equations), we deduce the initial and final value problems satisfied by the new convolution integrals.

Keywords

• Probability density
• convolution integral
• Fourier transform
• initial value problem
• final value problem