Geodesic
limit distributions of some Junctionals of a~stationary Gaussian process
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 2, pp. 236-249

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In this paper the limit distribution for sums $$ S_n=\sum_{k=1}^nf_{nk}(\xi_k^{(n)}) $$ is considered, where $f_{nk}(x)$ are measurable functions, $$ \xi_k^{(n)}=\xi\biggl(\frac knT\biggr)-\xi\biggl(\frac{k-1}nT\biggr),\quad k=1,2,\dots,n, $$ and $\xi(t)$, $t\in[0,T]$ is a stationary real-valued Gaussian process. Conditions are obtained under which the distributions of $S_k$ converge to a Gaussian and degenerate law. 
@article{TVP_1969_14_2_a4,
     author = {Yu. M. Ryzhov},
     title = {limit distributions of some {Junctionals} of a~stationary {Gaussian} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {236--249},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a4/}
}
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Yu. M. Ryzhov. limit distributions of some Junctionals of a~stationary Gaussian process. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 2, pp. 236-249. http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a4/