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

Andrey Pilipenko

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arXiv · 1306.0212

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

Andrey Pilipenko

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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 $\alpha\in(1;2)$, 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.

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Andrey Pilipenko. 2013-06-02. On existence and properties of strong solutions of one-dimensional stochastic equations with an additive noise. https://arxiv.org/abs/1306.0212

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