On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes

2010/11/02 by Fournier, Nicolas · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1011.0532

Abstract

We study a one-dimensional stochastic differential equation driven by a stable Lévy process of order α with drift and diffusion coefficients b,σ. When α∈ (1,2), we investigate pathwise uniqueness for this equation. When α∈ (0,1), we study another stochastic differential equation, which is equivalent in law, but for which pathwise uniqueness holds under much weaker conditions. We obtain various results, depending on whether α∈ (0,1) or α∈ (1,2) and on whether the driving stable process is symmetric or not. Our assumptions involve the regularity and monotonicity of b and σ.

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