The structure of martingales generated by restrictions on stochastically continuous fields with independent increments to curves. III. (Ukrainian, English) Zbl 1026.60067

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

Teor. Jmovirn. Mat. Stat. 65, 136-151 (2001); translation in Theory Probab. Math. Stat. 65, 153-170 (2002).

This article is the third part of articles by the authors [see Theory Probab. Math. Stat. 61, 137-152 (2000); translation from Teor. Jmovirn. Mat. Stat. 61, 131-144 (2000; Zbl 0986.60041) and ibid. 62, 113-126 (2001), resp. ibid. 62, 105-118 (2000; Zbl 1004.60053)]. In this part the authors find projections of a Wiener field on increasing ‘sewn’ curves. Properties of line stochastic integrals are investigated. The structure of martingales generated by the restriction of a Wiener field on piecewise monotone curves is described.

Reviewer: Mikhail Moklyachuk (Kyïv)

MSC:

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

Keywords:

martingales; random fields; fields with independent increments; Wiener fields; line stochastic integral; Brownian motion

Citations:

Zbl 0986.60041; Zbl 1004.60053