Equivalence of measures corresponding to solutions of some problems of mathematical physics with random Gaussian perturbation. (Russian) Zbl 0669.60046

Sokhadze, G. A.

Teor. Veroyatn. Mat. Stat., Kiev 39, 116-123 (1988).

In a Hilbert space H, the abstract equations \(Ax+B(x)=\xi\) and \(Ay=\xi\) are considered, where \(\xi\) is a Gaussian random variable, A is an unbounded linear operator in H and B a nonlinear operator. Let \(\mu_ x\) and \(\mu_ y\) be the distributions of the random variables x and y. In this paper conditions for \(\mu_ x\sim \mu_ y\) and the formula for the Radon-Nikodym density are given. Concrete applications in mathematical physics are given.

Reviewer: G.A.Sokhadze

MSC:

60G30	Continuity and singularity of induced measures
60K35	Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

equivalence of measures; Gaussian perturbation; Radon-Nikodym density; mathematical physics