科研成果详情

Let d ≥ 2. In this paper, we study weak solutions for the following type of stochastic differential equations: dXt = dSt + b(s + t,Xt)dt, t ≥ 0, X0 = x, where (s,x)∈ℝ+ × ℝd is the starting point, b: ℝ+ × ℝd → ℝd is measurable, and S = (St)t≥0 is a d-dimensional centered α-stable process with index α ∈ (1, 2). We show that if the centered α-stable process S is non-degenerate and b ∈ Lloc∞(ℝ+; L∞(ℝd)) + Llocq(ℝ+; Lp(ℝd)) for some p,q > 0 with d/p + α/q < α - 1, then the above SDE has a unique weak solution for every starting point (s,x) ∈ ℝ+ × ℝd.