Geodesic
Limit Theorems for Functionals of Sample Functions of a~Stationary Gaussian Process
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 2, pp. 370-372

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Let $\xi(t)$, $t\in[0,T]$, be a stationary Gaussian process with zero mean. We investigate the conditions for the functionals $$ S_n=\sum_{k=1}^nf_n\biggl(\xi\biggl(\frac knT\biggr)\biggr)\frac Tn $$ to converge to the additive functionals $$ J=\int_0^Tg(\xi(t))\,dt. $$ 
@article{TVP_1967_12_2_a14,
     author = {Yu. M. Ryzhov},
     title = {Limit {Theorems} for {Functionals} of {Sample} {Functions} of {a~Stationary} {Gaussian} {Process}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {370--372},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_2_a14/}
}
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Yu. M. Ryzhov. Limit Theorems for Functionals of Sample Functions of a~Stationary Gaussian Process. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 2, pp. 370-372. http://geodesic.mathdoc.fr/item/TVP_1967_12_2_a14/