Integration by parts formula for killed processes: A point of view from approximation theory

一维扩散过程退出时间的分部积分公式

Integration by parts formula for exit times of one dimensional diffusions

本文为一维扩散过程的首个退出时间建立了分部积分公式，采用基于时间变量的微积分技术，而非传统的空间马尔可夫链微分方法。

紧集与Lévy过程平衡测度的Tanaka型公式

A Tanaka-Type Formula for Compact Sets and Equilibrium Measures of Lévy Processes

将Tanaka公式从单点集推广到紧集，引入平衡测度并证明击中紧集的预势函数可分解为平衡测度积分与Robin常数之和，对区间情形给出显式表示。

A potential theoretic approach to Tanaka formula for asymmetric Lévy processes

In this paper, we shall introduce the Tanaka formula from viewpoint of the Doob-Meyer decomposition. For symmetric Lévy processes, if the local time exists, Salminen and Yor (2007) obtained the Tanaka formula by using the potential theoretic techniques. On the other hand, for asymmetric stable processes with index $α\in (1,2)$, we studied the Tanaka formula by using Itô's stochastic calculus and the Fourier analysis. In this paper, we study the Tanaka formula for asymmetric Lévy processes via the potential theoretic approach. We give several examples for important processes. Our approach also …

A probabilistic view on the deterministic mutation-selection equation: dynamics, equilibria, and ancestry via individual lines of descent

We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes ancestral (random) structures inherent in this deterministic model. In a first step, we obtain a representation of the deterministic equation's solution (and, in particular, of its equilibrium) in terms of an ancestral process called the killed ancestral selection graph. This representation allows one to understand the bifurcations related to the error thresho…

从泛函分析视角看黎曼流形中的随机积分

Stochastic integration in Riemannian manifolds from a functional-analytic point of view

本文从纯泛函分析视角构造黎曼流形上的随机积分，证明此类积分有无穷多个且任意两个可由简单公式联系，并指出Stratonovich积分和Itô积分是其特例。

广义Rough积分、Levy Rough路径和Levy-Kintchine型公式

General Rough integration, Levy Rough paths and a Levy--Kintchine type formula

我们考虑带跳跃的粗糙路径。特别地，在跳跃环境下建立了Lyons延拓定理和粗糙积分的类比，为随机积分的cadlag过程提供了一种途径性的观点.利用李群值Levy过程的Hunt框架，引入了一类Levy粗路，并刻画了其左不变扩散向量场上的次椭圆性条件和群上的Carnot-Caratheodory范数关于Levy测度的可积性. Levy粗路径的例子包括由D. Williams，磁场中的纯区域泊松过程和布朗运动。给出了期望签名的一个显式公式。