四边形内的布朗运动

象限中具有斜 Neumann 边界条件的 Green 函数

Green's Functions with Oblique Neumann Boundary Conditions in the Quadrant

本文研究了暂态情形下第一象限中带漂移的半鞅斜反射 Brown 运动，通过建立新的核函数方程并将其转化为非齐次 Carleman 边值问题，求得了该过程 Green 函数矩母函数的显式积分表达式。

Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant

We consider an obliquely reflected Brownian motion $Z$ with positive drift in a quadrant stopped at time $T$, where $T:=\inf \{ t>0 : Z(t)=(0,0) \}$ is the first hitting time of the origin. Such a process can be defined even in the non-standard case where the reflection matrix is not completely-$\mathcal{S}$. We show that in this case the process has two possible behaviors: either it tends to infinity or it hits the corner (origin) in a finite time. Given an arbitrary starting point $(u,v)$ in the quadrant, we consider the escape (resp. absorption) probabilities $\mathbb{P}_{(u,v)}[T=\infty]$ …

A two-dimensional oblique extension of Bessel processes

We consider a Brownian motion forced to stay in the quadrant by an electrostatic oblique repulsion from the sides. We tackle the question of hitting the corner or an edge, and find product-form stationary measures under a certain condition, which is reminiscent of the skew-symmetry condition for an obliquely reflected Brownian motion.

带斜反射的象限中布朗运动的轨道非唯一性

Pathwise non-uniqueness for Brownian motion in a quadrant with oblique reflection

本文研究闭第一象限中带斜反射的二维布朗运动 Skorokhod 方程，在特定角度和参数条件下证明一大类反射参数会导致轨道非唯一性。

随机环境中分支群体的共存

Co-existence of branching populations in random environment

本文研究联合随机环境中两个临界分支过程共存至大时间$n$的概率，证明其以$n^{-\ heta}$衰减，并给出条件极限定理，核心工具是二维随机游走正象限熵排斥的定性界。