ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE CAUCHY PROBLEM FOR WAVE EQUATIONS WITH GENERAL STOCHASTIC MEASURES

摘要

The existence and uniqueness of a solution of the Cauchy problem for wave equations containing a term expressed via the integral with respect to a stochastic measure are proved. Some general properties of generalized functions assuming values in a Fréchet space are used in the proof of the uniqueness of a solution.