Limit theorem for functionals of random walks. (Russian) Zbl 0644.60032

Girko, V. L.; Matvejchuk, A. K.

Teor. Veroyatn. Mat. Stat., Kiev 36, 33-36 (1987).

Let \(\{\xi_ n\}^{\infty}_{n=1}\) be independent random variables; \[ S_ n=\sum^{n}_{k=1}\xi_ k,\quad f(x)=\sum^{r}_{m=1}C_ m\exp (iU_ mx),\quad | C_ m| \leq C<\infty. \] Under some conditions on the characteristic functions of \(\xi_ n\), a limit theorem for the variables \(\nu_ n=\sum^{n}_{k=1}f(S_ n)\) is proved.

Reviewer: G.A.Sokhadze

MSC:

60F17	Functional limit theorems; invariance principles
60G50	Sums of independent random variables; random walks
60E10	Characteristic functions; other transforms

Keywords:

characteristic functions