Sufficient conditions of weak convergence of two-parameter semimartingales to fields of diffusion type. (Russian) Zbl 0671.60024

Mishura, Yu. S.

Teor. Veroyatn. Mat. Stat., Kiev 39, 97-106 (1988).

The paper contains limit theorems for weak and strong two-parameter semimartingales. Sufficient conditions for weak convergence to processes of diffusion type on the plane are given. They generalize corresponding results of R. Sh. Liptser and A. N. Shiryajev for one-parameter processes. The discrete scheme is also considered. The results are based on the canonical representation of two-parameter semimartingales.

Reviewer: Yu.S.Mishura

MSC:

60F17	Functional limit theorems; invariance principles
60G44	Martingales with continuous parameter
60G60	Random fields

Keywords:

diffusion process; weak and strong two-parameter semimartingales; weak convergence; canonical representation of two-parameter semimartingales