• Corpus ID: 118944492

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

@article{Pilipenko2013OnEA,
  title={On existence and properties of strong solutions of one-dimensional stochastic equations with an additive noise},
  author={Andrey Pilipenko},
  journal={arXiv: Probability},
  year={2013}
}
  • A. Pilipenko
  • Published 2 June 2013
  • Mathematics
  • arXiv: Probability
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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