Document Zbl 0681.60054

A comparison theorem for stochastic equations with Volterra drifts. (English) Zbl 0681.60054

Ann. Probab. 17, No. 4, 1541-1545 (1989).

Summary: A comparison theorem is proved for one-dimensional stochastic equations driven by continuous semimartingales and having Volterra-type drifts. A counterexample which shows that the coefficient of the continuous martingale term cannot be Volterra-type is given. Then the comparison result is used in order to obtain the existence of strong solutions when the Lipschitz condition is replaced by a Hölder-type one.

Cited in 1 Document

MSC:

60H20

Stochastic integral equations

Keywords:

strong solutions; Volterra drifts; comparison theorem; continuous martingale

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A comparison theorem for stochastic equations with Volterra drifts. (English) Zbl 0681.60054

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