On existence and properties of strong solutions of one-dimensional stochastic equations with an additive noise
Abstract
One-dimensional stochastic differential equations with additive L\'evy noise are considered. Conditions for existence and uniqueness of a strong solution are obtained. In particular, if the noise is a L\'evy symmetric stable process with α∈(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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