Stochastic differential equations in the plane that contain strong semimartingales. (English. Russian original) Zbl 0834.60063

Mishura, Yu. S.

Theory Probab. Math. Stat. 45, 77-85 (1992); translation from Teor. Veroyatn. Mat. Stat., Kiev 45, 79-88 (1991).

Summary: Sufficient conditions are obtained for the existence and uniqueness of a solution of a stochastic equation of the form \(x_t = H_t + ((f \circ x) \cdot z)_t\), \(t \in R^2_+\), where \(H_t\) and \(z_t\) are strong semimartingales, and \(f\) is a weakly predictable function.

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60G48	Generalizations of martingales

Keywords:

existence and uniqueness of a solution of a stochastic equation; weakly predictable function