Reflected Brownian motion in generic triangles and wedges

退化反射布朗运动在楔形中的马丁边界

Martin boundary of a degenerate Reflected Brownian Motion in a wedge

本文研究退化反射布朗运动在楔形中的马丁边界，通过计算格林函数的拉普拉斯变换并推导其渐进行为，确定了最小马丁边界及相应的调和函数。

楔形中的反射布朗运动：顶点处吸收概率的指数和形式与微分性质

Reflected Brownian Motion in a wedge: sum-of-exponential absorption probability at the vertex and differential properties

研究楔形中斜反射布朗运动的吸收概率，证明参数$α\in\mathbb{N}^*$是吸收概率可表示为指数乘积有限和的充要条件，并给出其Laplace变换的显式表达式。

Simultaneous boundary hitting by coupled reflected Brownian motions

(i) Uncountably many synchronized reflected Brownian motions can hit the boundary of a $C^2$ domain at the same time. (ii) Measures associated to local times of two synchronized reflected Brownian motions are mutually singular until the time when the normal vectors at the reflection locations become identical. (iii) Mirror coupled reflected Brownian motions can simultaneously hit opposite sides of a wedge at different distances from the origin.

关于楔形中反射布朗运动平稳分布的微分性质

On the stationary distribution of reflected Brownian motion in a wedge: differential properties

研究二维楔形中半鞅反射布朗运动平稳分布的Laplace变换的代数与微分性质，推导其成为有理式、代数式、微分有限或微分代数式的充要条件，并利用Tutte不变量方法和Galois理论给出简单表达式与证明。

Reflected planar Brownian motions, intertwining relations and crossing probabilities

Prompted by an example arising in critical percolation, we study some reflected Brownian motions in symmetric planar domains and show that they are intertwined with one-dimensional diffusions. In the case of a wedge, the reflected Brownian motion is intertwined with the 3-dimensional Bessel process. This implies some simple hitting distributions and sheds some light on the formula proposed by Watts for double-crossing probabilities in critical percolation.

随机Lipschitz系数下带违约时间的双重反射倒向随机微分方程：滤链与广义Dynkin博弈

Doubly reflected BSDEs with default time under stochastic Lipschitz coefficients: Filtration links and generalized Dynkin games

该研究在渐进扩大滤子下，针对带违约时间的随机Lipschitz系数DRBSDEs，建立解的存在唯一性，探讨其与参考滤子中方程的关系，并刻画了相关非线性Dynkin博弈的价值过程与鞍点。

A Dirichlet Process Characterization of RBM in a Wedge

Reflected Brownian motion (RBM) in a wedge is a 2-dimensional stochastic process Z whose state space in R^2 is given in polar coordinates by S={(r,theta): r >= 0, 0 <= theta <= xi} for some 0 < xi < 2 pi. Let alpha= (theta_1+theta_2)/xi, where -pi/2 < theta_1,theta_2 < pi/2 are the directions of reflection of Z off each of the two edges of the wedge as measured from the corresponding inward facing normal. We prove that in the case of 1 < alpha < 2, RBM in a wedge is a Dirichlet process. Specifically, its unique Doob-Meyer type decomposition is given by Z=X+Y, where X is a two-dimensional Brown…

Multidimensional sticky Brownian motions as limits of exclusion processes

We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and the entire particle system is slowed down until the ``collision'' is resolved. We show that under diffusive scaling of space and time such processes converge to what one might refer to as a sticky reflected Brownian motion in the wedge. The latter behaves as a Brownian motion with constant drift vector and diffusion matrix in the interior of the wedge, and ref…

随机时域市场中由脆弱索赔引出的线性反射倒向随机微分方程

Linear reflected backward stochastic differential equations arising from vulnerable claims in markets with random horizon

本文研究随机时域市场中脆弱索赔对冲所引出的线性反射倒向随机微分方程，在不忽略随机时间自身风险的条件下，给出解存在的最小充分条件、解的范数估计，并建立其与一个密切相关的F-RBSDE之间的联系。

反射 Lévy 游荡的进入律的局部渐近性

Local Asymptotics for Entrance Laws of Reflected Lévy Excursions

本文针对反射 Lévy 游荡的进入律，建立了固定时间和长时间两种范围内的一致局部大偏差渐近公式，并推广到首次低于零被杀死的 Lévy 过程。

动态Erdős-Rényi随机图中连通时间与断开时间分布的估计

Estimation of on- and off-time distributions in a dynamic Erdős-Rényi random graph

针对仅能观测边总数的动态Erdős-Rényi图，提出基于矩法的参数化估计量以估计边的连通/断开时间分布，证明其渐近正态性并给出协方差辨识方法，还可适配楔形、三角形等其他子图计数观测场景。