论文标题
Wasserstein的距离估算值
Wasserstein distance estimates for jump-diffusion processes
论文作者
论文摘要
我们在随机积分（ITô）过程的概率分布之间取得了wasserstein的距离界限，该过程与跳跃$（x_t）_ {t \ in [0，t]} $与跳跃 - 扩散过程$（x^\ ast_t）_ {t \ in [0，t]} $。我们的边界是使用$（x_t）_ {t \ in [0，t]} $的随机特性和$（x^\ ast_t）_ {t \ in [0，t]} $的$（x^\ ast_t）$的跳转系数的$（x^\ ast_t）} $特别适用于$ x_t $的$（x^\ ast_t）_ {我们的方法使用随机演算参数和$ l^p $的集成性结果，用于跳跃随机微分方程的流动，而无需依赖Stein方程。
We derive Wasserstein distance bounds between the probability distributions of a stochastic integral (Itô) process with jumps $(X_t)_{t\in [0,T]}$ and a jump-diffusion process $(X^\ast_t)_{t\in [0,T]}$. Our bounds are expressed using the stochastic characteristics of $(X_t)_{t\in [0,T]}$ and the jump-diffusion coefficients of $(X^\ast_t)_{t\in [0,T]}$ evaluated in $X_t$, and apply in particular to the case of different jump characteristics. Our approach uses stochastic calculus arguments and $L^p$ integrability results for the flow of stochastic differential equations with jumps, without relying on the Stein equation.
