International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 549-558
doi:10.1155/S0161171280000415

Generalized random processes and Cauchy's problem for some partial differential systems

Abstract

In this paper we consider a parabolic partial differential system of the form DtHt=L(t,x,D)Ht. The generalized stochastic solutions Ht, corresponding to the generalized stochastic initial conditions H0 are given. Some properties concerning these generalized stochastic solutions are also obtained.