平稳分枝超Lévy过程是一个随机偏微分方程的轨道唯一解

Stable branching super-Lévy process as the pathwise unique solution to an SPDE

本文证明平稳(stable)分枝超Lévy过程的密度在一定条件下是如下随机偏微分方程的轨道唯一解:?/?tX_t(x)=AX_t(x)+bX_t(x)+X_(t-)(x)α/1■_t(x), t> 0, x∈R,其中A是超Lévy过程底运动的生成元,α∈(1, 2)和b∈R是常数,{■_t(x):t≥0, x∈R}是一个无负跳的单边的α-平稳噪声.

In this paper,we show that the density of a stable branching super-Lévy process is the pathwise unique solution to?/?tXt(x)=AXt(x)+bXt(x)+Xt-(x)α/1Lt(x),t>0,x∈R tunder certain conditions,where A is the generator of a Lévy process,α∈(1,2)and b∈R are constants,and{Lt(x):t≥0,x∈R}is a one sidedα-stable noise without negative jumps.This partly generalizes the recent work of Yang and Zhou(2017),in which A=?/2(?denotes the Laplacian operator)was considered.