可分巴拿赫空间中随机测度驱动的抽象Cauchy问题：有限灭绝情形的渐近结果
Abstract Cauchy Problems in separable Banach Spaces driven by random Measures: Asymptotic Results in the finite extinction Case
摘要：
本文的目的是证明一类向量值随机过程的强大数律和中心极限定理，这类随机过程是随机发展包含\begin{align*} η(t,z) N_Θ(dt \otimes z)\in dX(t)+\mathcal{A} X(t)dt, \end{align*}的解，其中$\mathcal{A}$是多值算子，$N_Θ$是由点过程$Θ$诱导的计数测度. SLLN和CLT将被证明不仅为实值，而且为向量值泛函和这些结果的适用性（加权）$p$ -拉普拉斯发展方程（“小”$p$）将被证明。本文的关键假设是由多值算子$\mathcal{A}$生成的非线性半群在有限时间内收敛。
英文摘要：
The aim of this paper is to prove the strong law of large numbers (SLLN) as well as the central limit theorem (CLT) for a class of vector-valued stochastic processes which arise as solutions of the stochastic evolution inclusion \begin{align*} η(t,z) N_Θ(dt \otimes z)\in dX(t)+\mathcal{A} X(t)dt, \end{align*} where $\mathcal{A}$ is a multi-valued operator and $N_Θ$ is the counting measure induced by a point process $Θ$. The SLLN and the CLT will be proven not only for real-valued, but also for vector-valued functionals and the applicability of these results to the (weighted) $p$-Laplacian evolution equation (for "small" $p$) will be demonstrated. The key assumption needed in this paper is that the nonlinear semigroup arising from the multi-valued operator $\mathcal{A}$ extincts in finite time.
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