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Short Communications

The action functional for a class of stochastic processes

M. I. Freidlin

Moscow

Abstract: Let $x_t$ be a Gaussian process with zero mean and correlation operator $A$. The action functional for this process is defined by the equality $S(\varphi)=(A^{-1/2}\varphi,A^{-1/2}\varphi)$. We prove a number of theorems concerning action functionals which enable us to solve some asymptotic problems for Gaussian processes and processes obtained from Gaussian ones by nonlinear transforms.

Received: 18.11.1970

 English version: Theory of Probability and its Applications, 1973, 17:3, 511–515

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