Conditions for uniform convergence of \(\overline{\text{Sub}}_ \varphi (\Omega)\)-stochastic integrals. (English. Ukrainian original) Zbl 0842.60053

Kozachenko, Yu. V.; Endzhyrgly, M. V.

Theory Probab. Math. Stat. 48, 47-54 (1994); translation from Teor. Jmovirn. Mat. Stat. 48, 67-77 (1993).

Summary: Stochastic integrals \(\int^\infty_0 T(t, \lambda) d\eta (\lambda)\) are considered in which the stochastic process \(\eta (\lambda)\) belongs to the space \(\overline {\text{Sub}}_\varphi (\Omega)\). Certain conditions for uniform convergence in probability and estimates for the distribution of the supremum of these integrals are described.

MSC:

60H05	Stochastic integrals
60G70	Extreme value theory; extremal stochastic processes

Keywords:

stochastic integrals; uniform convergence in probability