Stochastic approach for the subordination in Bochner sense

Bochner's Subordionation and Fractional Caloric Smoothing in Besov and Triebel--Lizorkin Spaces

We use Bochner's subordination technique to obtain caloric smoothing estimates in Besov- and Triebel--Lizorkin spaces. Our new estimates extend known smoothing results for the Gauß--Weierstraß, Cauchy--Poisson and higher-order generalized Gauß--Weierstraß semigroups. Extensions to other function spaces (homogeneous, hybrid) and more general semigroups are sketched.

On subordinate random walks

In this article subordination of random walks in $R^d$ is considered. We prove that subordination of random walks in the sense of [BSC12] yields the same process as subordination of Lévy processes (in the sense of Bochner). Furthermore, we prove that appropriately scaled subordinate random walk converges to a multiple of a rotationally $2α$-stable process if and only if the Laplace exponent of the corresponding subordinator varies regularly at zero with index $α\in (0,1]$.

Thorin过程及其从属化

Thorin processes and their subordination

本文研究Thorin过程的结构与性质关系，发现Thorin测度支集刻画临界指数矩和渐近等价性，并利用Thorin-Bondesson表示简化布朗从属化公式，全面阐述多元Thorin过程理论及伽马过程的负二项从属化。

若干复合过程的积分

Integrals of some compound processes

该研究基于复合泊松过程理论构建通用框架，证明伯恩斯坦从属的时间变换性质，推导复合过程积分的显式表示等结果，为相关随机过程研究提供理论支撑。