On existence and properties of strong solutions of one-dimensional stochastic equations with an additive noise

Abstract

One-dimensional stochastic differential equations with additive Lévy noise are considered. Conditions for existence and uniqueness of a strong solution are obtained. In particular, if the noise is a Lévy symmetric stable process with $\alpha \in (1;2)$, then the measurability and boundedness of a drift term is sufficient for the existence of a strong solution. We also study continuous dependence of the strong solution on the initial value and the drift.

6 pages; to appear in Theory of Stochastic Processes

Cited by in corpus (1)

• A comparison theorem for stochastic differential equations under a Novikov-type condition