Efficient evaluation of expectations of functions of a stable Lévy process and its extremum

Lévy过程及其极值函数期望的高效计算

Efficient evaluation of expectations of functions of a Lévy process and its extremum

本文推导了Lévy过程及其运行极值函数期望的通用公式，结合Fourier/Laplace反演与Wiener-Hopf分解，利用sinh加速技术等高效数值方法实现了高精度快速计算。

次线性期望下α-稳定中心极限定理的收敛速度

On the rate of convergence for an $α$-stable central limit theorem under sublinear expectation

本文通过构造单调逼近格式并建立误差界，给出了次线性期望下α-稳定中心极限定理的显式Berry-Esseen界和收敛速度。

An $α$-stable limit theorem under sublinear expectation

For $α\in (1,2)$, we present a generalized central limit theorem for $α$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential equations (PIDEs). A classical generalized central limit theorem is recovered as a special case, provided a mild but natural additional condition holds. Our approach contrasts with previous arguments for the result in the linear setting which have typically relied upon tools that are non-existent in the sublinear framework, for example, characteristic functions.

A robust $α$-stable central limit theorem under sublinear expectation without integrability condition

This article relaxes the integrability condition imposed in the literature for the robust $α$-stable central limit theorem under sublinear expectation. Specifically, for $α\in(0,1]$, we prove that the normalized sums of i.i.d. non-integrable random variables $\big \{n^{-\frac{1}α}\sum_{i=1}^{n}Z_{i}\big \}_{n=1}^{\infty}$ converge in distribution to $\tildeζ_{1}$, where $(\tildeζ_{t})_{t\in \lbrack0,1]}$ is a multidimensional nonlinear symmetric $α$-stable process with a jump uncertainty set $\mathcal{L}$. The limiting $α$-stable process is further characterized by a fully nonlinear partial in…

A correlation inequality for the expectations of norms of stable vectors

For $0<q\le 2,\ 1\le k < n,$ let $X=(X_1,...,X_n)$ and $Y=(Y_1,...,Y_n)$ be symmetric $q$-stable random vectors so that the joint distributions of $X_1,...,X_k$ and $X_{k+1},...,X_n$ are equal to the joint distributions of $Y_1,...,Y_k$ and $Y_{k+1},...,Y_n,$ respectively, but $Y_i$ and $Y_j$ are independent for every $1\le i \le k,\ k+1\le j \le n.$ We prove that $\Bbb E (f(X)) \ge \Bbb E (f(Y))$ where $f$ is any continuous, positive, homogeneous of the order $p\in (-n,0)$ function on $\Bbb R^n\setminus \{0\}$ such that $f$ is a positive definite distribution in $\Bbb R^n,$ and $f(u,v)=f(u,-v…

α-稳定 Lévy 过程的局部时与占用时测度的最优估计

Optimal estimation of local time and occupation time measure for an α-stable Levy process

本研究针对α∈(1,2)的α-稳定Lévy过程，提出基于高频数据条件期望的L²最优局部时与占用时测度估计方法，证明了稳定中心极限定理，拓展了布朗运动情形下的已有结果。