The limit of integral sums and functionals of Lévy-Baxter type. (English. Russian original) Zbl 0639.60041

Kurchenko, A. A.

Theory Probab. Math. Stat. 33, 59-63 (1986); translation from Teor. Veroyatn. Mat. Stat. 33, 53-57 (1985).

Summary: Conditions are given for convergence in \(L_ 4\) of Baxter-type functionals of a vector-valued Gaussian random process. Mean-square limits are studied for integral sums of a random process continuous in the \(L_ 4\)-norm with respect to a vector-valued Gaussian random process of Gladyshev type. The results obtained are used to derive an analogue of the Itô formula.

MSC:

60F25	\(L^p\)-limit theorems
60H05	Stochastic integrals
60G15	Gaussian processes

Keywords:

Baxter-type functionals; vector-valued Gaussian random process; Gaussian random process of Gladyshev type; Itô formula