On one-dimensional stochastic differential equations with generalized drift. (English) Zbl 0583.60052

Stochastic differential systems, Proc. IFIP-WG 7/1 Work. Conf., Marseille-Luminy/France 1984, Lect. Notes Control Inf. Sci. 69, 143-155 (1985).
[For the entire collection see Zbl 0552.00009.]
The authors consider the one-dimensional stochastic differential equation with drift described by local time and signed measure. They give necessary and sufficient conditions for the existence and uniqueness of a solution of such equations. Also a sufficient condition for the existence of a pathwise unique strong solution is obtained.
Reviewer: A.D.Borisenko


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J55 Local time and additive functionals


Zbl 0552.00009