Geodesic
The action functional for a~class of stochastic processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 3, pp. 536-541

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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. 
@article{TVP_1972_17_3_a10,
     author = {M. I. Freidlin},
     title = {The action functional for a~class of stochastic processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {536--541},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_3_a10/}
}
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M. I. Freidlin. The action functional for a~class of stochastic processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 3, pp. 536-541. http://geodesic.mathdoc.fr/item/TVP_1972_17_3_a10/