Characteristic functionals of randomly excited physical systems (Q1079880)

This paper deals with characteristic functionals of the solutions of a wide class of stochastic differential equations describing random physical processes. First, a construction of the characteristic functional is shown in a general case of the stochastic evolution equation in Hilbert space. Then making use of the construction presented, the analysis of three random physical processes is performed: the random harmonic oscillator, random wave process and random heat conduction. Special attention in these applications is focused on the cases where an excitation process has the form of a sequence of randomly arriving impulses.