On a functional limit theorem for time series constructed from shot noise processes. (English. Ukrainian original) Zbl 0990.60028

Buldygin, V. V.; Il’jenko, A. B.

Theory Probab. Math. Stat. 63, 21-25 (2001); translation from Teor. Jmovirn. Mat. Stat. 63, 21-25 (2000).

Let \(\zeta(s)\), \(s\in R\), \(\zeta(0)=0,\) be a stochastically continuous homogeneous random process with independent increments without Gaussian component and let \(\theta(t)=\int_{-\infty}^{\infty}g(t-s) d\zeta(s)\), \(g\in L_2(R)\). The authors study convergence of the random process \(\Theta_{n}(t)=n^{-1/2}\sum_{k=1}^{[nt]}\theta(kh)\), \(t\in [0,1], n\to\infty,\) to the Wiener process in the space \(D[0,1]\) of functions without discontinuity of the second kind with the Skorokhod topology.

Reviewer: A.D.Borisenko (Kyïv)

MSC:

60F17

Functional limit theorems; invariance principles

Keywords:

functional limit theorem; time series; shot noise process; process with independent increments; Wiener process; Skorokhod topology