论文标题
它{之一的公式用于泊松随机积分和应用的度量
It{ô}'s formula for the flow of measures of Poisson stochastic integrals and applications
论文作者
论文摘要
我们证明了它{}的公式，用于与漂移定义的跳跃过程相关的度量流，这是泊松随机度量以及相关补偿的泊松随机度量的积分。我们在$ \ mathcal {p}_β（\ Mathbb {r}^d）$中工作，$ \ Mathbb {r}^d $具有有限的订单$β\ in（0，2] $的有限级时刻$β\的概率度量的空间\ Mathcal {p}_β（\ Mathbb {r}^d）$与McKean-Vlasov随机度量驱动的McKean-Vlasov随机微分方程相关，它描述了与McKean-Vlasov随机差异方程相关的半群落的动力。混乱的新定量弱传播结果是由I.I.D驱动的相互作用的Ornstein-uhlenbeck相互作用的过程。
We prove It{ô}'s formula for the flow of measures associated with a jump process defined by a drift, an integral with respect to a Poisson random measure and with respect to the associated compensated Poisson random measure. We work in $\mathcal{P}_β(\mathbb{R}^d)$, the space of probability measures on $\mathbb{R}^d$ having a finite moment of order $β\in (0, 2]$. As an application, we exhibit the backward Kolmogorov partial differential equation stated on $[0,T] \times \mathcal{P}_β(\mathbb{R}^d)$ associated with a McKean-Vlasov stochastic differential equation driven by a Poisson random measure. It describes the dynamics of the semigroup associated with the McKean-Vlasov stochastic differential equation, under regularity assumptions on it. Finally, we use the semigroup and the backward Kolmogorov equation to prove new quantitative weak propagation of chaos results for a mean-field system of interacting Ornstein-Uhlenbeck processes driven by i.i.d. $α$-stable processes with $α\in (1,2)$.
