On strong existence and continuous dependence for solutions of one-dimensional stochastic equations with additive Lévy noise

A. Yu. Pilipenko

Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereshchenkivska Str., Kyiv 01601, Ukraine

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

Keywords: Stochastic flow, local times, differentiability with respect to initial data.

MSC: Primary 60H10; Secondary 60J75

Language: English

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