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

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 $α\in(1;2)$, 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.

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