Volterra equations driven by semimartingales. (English) Zbl 0567.60065

Protter, Philip

Ann. Probab. 13, 519-530 (1985).

In modelling systems corrupted by noise, stochastic integral equations of Volterra type arise. M. A. Berger and V. J. Mizel [J. Integral Equations 2, 187-245 and 319-337 (1980; Zbl 0442.60064 and Zbl 0452.60073, resp.)] handled the white noise case and conjectured that their results could be extended to the case when Brownian motion is replaced by right continuous semimartingales. The author obtains an existence and uniqueness theorem for these Volterra equations, thereby establishing the Berger-Mizel conjecture.

Reviewer: J.A.Goldstein

MSC:

60H20	Stochastic integral equations
45E99	Singular integral equations
60H05	Stochastic integrals
60G48	Generalizations of martingales

Keywords:

stochastic integral equations of Volterra type; existence and uniqueness theorem

Citations:

Zbl 0442.60064; Zbl 0452.60073