Geodesic
On strong existence and continuous dependence for solutions of one-dimensional stochastic equations with additive L\'evy noise
Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 77-82

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One-dimensional stochastic differential equations (SDEs) with additive Lévy noise are considered. Conditions for strong existence and uniqueness of a solution are obtained. In particular, if the noise is a Lévy symmetric stable process with $\alpha\in(1;2),$ then the measurability and the boundedness of a drift term is sufficient for the existence of a strong solution. We also study the continuous dependence of the strong solution on the initial value and the drift.
Keywords: Stochastic flow, local times, differentiability with respect to initial data. 
@article{THSP_2012_18_2_a7,
     author = {A. Yu. Pilipenko},
     title = {On strong existence and continuous dependence for solutions of one-dimensional stochastic equations with additive {L\'evy} noise},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {77--82},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a7/}
}
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A. Yu. Pilipenko. On strong existence and continuous dependence for solutions of one-dimensional stochastic equations with additive L\'evy noise. Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 77-82. http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a7/