科研成果详情

Let d≥ 1. Consider a stable-like operator of variable order Af(x)=∫Rd\{0}[f(x+h)-f(x)-1{|h|≤1}h·∇f(x)]n(x,h)|h|-d-α(x)dh,where 0 < inf α(x) ≤ sup α(x) < 2 and n(x, h) satisfies n(x,h)=n(x,-h),0<κ1≤n(x,h)≤κ2,∀x,h∈Rd,with κ and κ being some positive constants. Under some further mild conditions on the functions n(x, h) and α(x) , we show the uniqueness of solutions to the martingale problem for A.