The structure of martingales generated by restrictions of stochastically continuous fields with independent increments to curves. II. (English. Ukrainian original) Zbl 1004.60053

Mishura, Yu. S.; Zolota, A. V.

Theory Probab. Math. Stat. 62, 113-126 (2001); translation from Teor. Jmovirn. Mat. Stat. 62, 105-118 (2000).

This article is the second part of the article [Theory Probab. Math. Stat. 61, 137-152 (2000); translation from Teor. Jmovirn. Mat. Stat. 61, 131-144 (2000; Zbl 0986.60041)].
Martingales generated by the restriction of a Wiener field on a finite number of increasing curves are considered. The projections of this Wiener field on the respective curves are found and a representation of the martingale given on some flow of \(\sigma\)-algebra generated by the restriction of the Wiener field on these curves is given. This representation is given in form of a sum of line stochastic integrals. Examples of calculation of integrands with the help of the system of ordinary differential equations are proposed.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

60G60	Random fields
60J65	Brownian motion
60G44	Martingales with continuous parameter

Keywords:

martingales; fields with independent increments; Wiener fields; line stochastic integrals

Citations:

Zbl 0986.60041