各向同性布朗流作用下的体积弥散

两个各向同性分数布朗运动场最大值平方增量和的极限定理（固定域渐近情形）

Limit theorems for squared increment sums of the maximum of two isotropic fractional Brownian fields under fixed-domain asymptotics

研究两个独立同分布各向同性分数布朗运动场在固定二维域上的点wise最大值的平方增量和，揭示其在Hurst参数H<1/2时的渐近行为，证明归一化后收敛于确定常数乘以两个场差的局部时间。

对“斜布朗运动的占位时和局部时及其在界面色散中的应用”的修正

Corrections for "Occupation and local times for skew Brownian motion with applications to dispersion across an interface"

我们正在进行更正，并感谢同事指出我们最近发表在Annals of Applied Probability（2011）21（1）183-214上的题为“Occupation and local times for skew布朗运动with applications to dispersion across an interface”的论文中的错误。具体的更正是：1。不需要定理1.3中将$γ$限制为非负值。但只有当$γ$为非负时才有概率解释。2.说明推论3.3中的正确公式，因为它们是原始公式中的计算错误。我们感谢Pierre Etoiré和Miguel Martinez指出这些错误。

The Doob-McKean identity for stable Lévy processes

We re-examine the celebrated Doob--McKean identity that identifies a conditioned one-dimensional Brownian motion as the radial part of a 3-dimensional Brownian motion or, equivalently, a Bessel-3 process, albeit now in the analogous setting of isotropic $α$-stable processes. We find a natural analogue that matches the Brownian setting, with the role of the Brownian motion replaced by that of the isotropic $α$-stable process, providing one interprets the components of the original identity in the right way.

球面上的各向同性 Q-分数布朗运动：正则性与快速模拟

Isotropic Q-fractional Brownian motion on the sphere: regularity and fast simulation

本文提出球面上各向同性 Q-分数布朗运动，证明其时空 Hölder 正则性，用谱方法近似并证明收敛，通过循环嵌入或条件化随机中点位移快速模拟，数值验证了时间精度与复杂度。

Weak synchronization for isotropic flows

We study Brownian flows on manifolds for which the associated Markov process is strongly mixing with respect to an invariant probability measure and for which the distance process for each pair of trajectories is a diffusion $r$. We provide a sufficient condition on the boundary behavior of $r$ at $0$ which guarantees that the statistical equilibrium of the flow is almost surely a singleton and its support is a weak point attractor. The condition is fulfilled in the case of negative top Lyapunov exponent, but it is also fulfilled in some cases when the top Lyapunov exponent is zero. Particular…

Exit Laws of Isotropic Diffusions in Random Environment from Large Domains

This paper studies, in dimensions greater than two, stationary diffusion processes in random environment which are small, isotropic perturbations of Brownian motion satisfying a finite range dependence. Such processes were first considered in the continuous setting by Sznitman and Zeitouni [20]. Building upon their work, it is shown by analyzing the associated elliptic boundary-value problem that, almost surely, the smoothed (in the sense that the boundary data is continuous) exit law of the diffusion from large domains converges, as the domain's scale approaches infinity, to that of a Brownia…

On the Exit Time and Stochastic Homogenization of Isotropic Diffusions in Large Domains

Stochastic homogenization is achieved for a class of elliptic and parabolic equations describing the lifetime, in large domains, of stationary diffusion processes in random environment which are small, statistically isotropic perturbations of Brownian motion in dimension at least three. Furthermore, the homogenization is shown to occur with an algebraic rate. Such processes were first considered in the continuous setting by Sznitman and Zeitouni [21], upon whose results the present work relies strongly, and more recently their smoothed exit distributions from large domains were shown to conver…

二维空间中基于德劳内三角剖分的分数布朗运动平方增量和的中心极限定理

Central limit theorems for squared increment sums of fractional Brownian fields based on a Delaunay triangulation in $2D$

研究在单位正方形内由泊松点过程生成的点集，基于德劳内三角剖分考虑归一化增量和，推导当点密度趋于无穷时的中心极限定理。

各向同性Ornstein-Uhlenbeck流

Isotropic Ornstein-Uhlenbeck flows

各向同性布朗流（IBFs）是一类相当自然的随机流，已被许多作者广泛研究。它们丰富的结构允许在几种情况下进行显式计算，如果人们想研究更一般的随机流，就可以从它们开始。通过理解IBF背景下的问题而获得的直觉往往转移到更一般的情况。然而，随机流之间的明显联系，随机动力系统和遍历论不能充分利用其实力的IBF没有一个不变的概率测度，而是一个无限的。各向同性Ornstein-Uhlenbeck流在某种意义上是定域的IBF，并且具有不变的概率测度。施加的线性漂移破坏了IBF的平移不变性，但许多其他重要的结构性质，如距离过程的马尔可夫性仍然有效，并允许在某些情况下进行显式计算。各向同性的Ornstein-Uhlenbeck流具有不变的概率测度，这一事实允许人们应用随机动力系统理论的技术。我们证明了这一点，通过应用Ledrappier和Young的结果来计算各向同性Ornstein-Uhlenbeck流的统计平衡的豪斯多夫维数。

各向同性 Lévy 过程谱热含量小时间行为的统一方法

A unified approach to the small-time behavior of the spectral heat content for isotropic Lévy processes

本文针对特征指数在无穷远正则变化的各向同性 Lévy 过程，给出有界 C^{1,1} 区域上谱热含量的精确小时间渐近，并证明其对 Lévy 测度可积扰动的稳定性，统一涵盖 Brown 运动、稳定过程与跳扩散。

On the exact asymptotics of exit time from a cone of an isotropic $α$-self-similar Markov process with a skew-product structure

In this paper we identify the asymptotic tail of the distribution of the exit time $τ_C$ from a cone $C$ of an isotropic $α$-self-similar Markov process $X_t$ with a skew-product structure, that is $X_t$ is a product of its radial process and independent time changed angular component $Θ_t$. Under some additional regularity assumptions, the angular process $Θ_t$ killed on exiting from the cone $C$ has the transition density that could be expressed in terms of a complete set of orthogonal eigenfunctions with corresponding eigenvalues of an appropriate generator. Using this fact and some asympto…

粗糙情形下小噪声渐近的分数布朗运动随机微分方程的最大似然型估计量

The maximum likelihood type estimator of SDEs with fractional Brownian motion under small noise asymptotics in the rough case

针对分数布朗运动驱动的随机微分方程，在漂移和扩散系数满足一定假设时，构造最大似然估计量，证明小噪声下漂移参数的渐近正态性与矩收敛。