Strong existence and uniqueness for stable stochastic differential equations with distributional drift

2018/01/10 by Athreya, Siva, Butkovsky, Oleg, Mytnik, Leonid · 2 citations
#60G52 #60H10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1801.03473

Abstract

We consider the stochastic differential equation dX_t = b(X_t) dt + dL_t, where the drift b is a generalized function and L is a symmetric one dimensional α-stable Lévy processes, α∈ (1, 2). We define the notion of solution to this equation and establish strong existence and uniqueness whenever b belongs to the Besov--Hölder space C^β for β>1/2-α/2.

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