On Volterra type stochastic integrals with respect to a continuous strong martingale. (English) Zbl 0988.60043

Kolodij, Natalia A.

Theory Stoch. Process. 6(22), No. 1-2, 58-61 (2000).

The author deals with stochastic integrals with respect to two-parameter continuous strong square-integrable martingales whose integrands depend on limits of integration. Existence of a continuous modification of the Volterra type stochastic integral is proved under conditions which contain weaker regularity condition than the Hölder condition. An inequality for moments of continuous modifications of such integrals is proposed. For more details see, for example, A. M. Kolodij [Theory Stoch. Process. 4(20), No. 1-2, 133-138 (1998; Zbl 0939.60072)] and Yu. S. Mishura [Theory Probab. Math. Stat. 49, 123-136 (1994); translation from Teor. Jmovirn. Mat. Stat. 49, 173-192 (1993; Zbl 0861.60067)].

Reviewer: Mikhail Moklyachuk (Kyïv)

MSC:

60G48	Generalizations of martingales
60H05	Stochastic integrals
60G60	Random fields

Keywords:

strong martingale; stochastic integral; continuous modification; inequality for moments

Citations:

Zbl 0939.60072; Zbl 0681.60067; Zbl 0861.60067