Pathwise uniqueness for singular SDEs driven by stable processes

2010/05/23 by Priola, Enrico · 1 citation
#34F05 #35B65 #60H10 #60J75 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1005.4237

Abstract

We prove pathwise uniqueness for stochastic differential equations driven by non-degenerate symmetric α-stable Lévy processes with values in \R^d having a bounded and β-Hölder continuous drift term. We assume β> 1 - \fracα2 and α∈ [ 1, 2). The proof requires analytic regularity results for associated integro-differential operators of Kolmogorov type. We also study differentiability of solutions with respect to initial conditions and the homeomorphism property.

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• Strong and weak well-posedness of McKean-Vlasov SDEs driven by α-stable processes under unified condition

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