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One-dimensional stochastic differential equations with additive L\'evy noiseare considered. Conditions for existence and uniqueness of a strong solutionare obtained. In particular, if the noise is a L\'evy symmetric stable processwith $\alpha\in(1;2)$, then the measurability and boundedness of a drift termis sufficient for the existence of a strong solution. We also study continuousdependence of the strong solution on the initial value and the drift.

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