On Weak Solutions of SDEs with Singular Time-Dependent Drift and Driven by Stable Processes

2015/12/08 by Jin, Peng
#60H10 #60J75 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1512.02689

Abstract

Let d ≥ 2. In this paper, we study weak solutions for the following type of stochastic differential equation dX_t=dS_t+b(s+t, X_t)dt, X₀=x, where (s,x)∈ ℝ₊ × ℝ^d is the initial starting point, b: ℝ₊ × ℝ^d → ℝ^d is measurable, and S=(S_t)_{t ≥ 0} is a d-dimensional α-stable process with index α∈ (1,2). We show that if the α-stable process S is non-degenerate and b ∈ L_loc^∞(ℝ₊;L^∞(ℝ^d))+ L_loc^q(ℝ₊;L^p(ℝ^d)) for some p,q>0 with d/ p+α/q

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