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

Engelbert, H. J.; Schmidt, W.

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

MSC:

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

Keywords:

local time; existence and uniqueness of a solution; pathwise unique strong solution

Citations:

Zbl 0552.00009