时空相互作用下Infinite-dimensional扩散方程的短时Gibbsianness性

平均场相互作用布朗运动的Gibbs-非Gibbs动力学跃迁

Gibbs-non-Gibbs dynamical transitions for mean-field interacting Brownian motions

我们考虑一个系统的实值自旋相互作用，通过平均场哈密顿依赖于经验磁化的自旋通过一般的潜力。系统服从随机动力学，其中自旋执行独立的布朗运动。在\cite{FedHoMa13}中，考虑了居里-外斯模型，伊辛自旋通过二次势相互作用，并受到独立的自旋翻转，我们遵循\cite{vEFedHoRe10}中概述的程序。我们表明，在热力学极限的系统是非吉布斯在时间$t \in (0,\infty)$当且仅当存在一个$α\in \mathbb{R}$，使大偏差率函数的磁化条件的轨迹上击中值$α$在时间$t$有多个全球最小值。我们进一步表明，不同的最小化轨迹是不同的时间$t=0$。我们给出了系统在$t=0$时刻为Gibbs的势的条件，根据势的二阶差商对系统在$t \in (0,\infty)$时刻为Gibbs的可能情形进行了分类，并证明了系统一旦成为非Gibbs就不能成为Gibbs，即，从吉布斯到非吉布斯存在唯一且明确可计算的交叉时间$t_c \in [0,\infty]$。我们给出了立即失去吉布斯性（$t_c=0$）、短期保持吉布斯性、长期失去吉布斯性（$t_c\in (0,\infty)$）和保持吉布斯性（$t_c=\infty$）的例子。根据电势，系统在交叉时间$t=t_c$可以是吉布斯或非吉布斯。

平面渗流中IIC的简短定量构造

Short, Quantitative Construction of the IIC in Planar Percolation

通过引入无偏渗流构型耦合不同半径条件渗流，利用对偶单臂概率给出全变差距离收敛速度上界，在平面图上构造了初始无限团簇（IIC）。

关于无穷方差随机变量序列的$α$ -协方差、长记忆、短记忆和负记忆

On $α$-covariance, long, short and negative memories for sequences of random variables with infinite variance

本文考虑对称$α$ -稳定随机向量的依赖性测度，这是作者在1976年提出的。我们证明，这种措施的依赖性可以扩展到更广泛的一类随机向量（可分巴拿赫空间中的经常变化的向量）。该测度被应用于线性随机过程和重尾新息场，以及一些稳定过程，这些应用表明，这种相关测度（称为$α$ -协方差）是通常的协方差的一个很好的替代.此外，我们讨论了一个问题，定义长，短，和负记忆的平稳过程和领域的无穷方差。

Reflected backward stochastic differentialequation with jumps and viscosity solution of second order integro-differential equation without monotonicity condition: case with the measure of Levy infinite

We consider the problem of viscosity solution of integro-partial differential equation(IPDE in short) with one obstacle via the solution of reflected backward stochastic differential equations(RBSDE in short) with jumps. We show existence and uniqueness of a continuous viscosity solution of equation with non local terms, in case the generator is not monotonous and Levy's measure is infinite.

Exponential Quadratic BSDEs with infinite activity Jumps

In this paper, we study a Backward Stochastic Differential Equation with Jumps (BSDEJs in short) where the jumps have infinite activity. Following a forward approach based on Exponential Quadratic semimartingale, we prove the existence of solution of Quadratic BSDEJs with unbounded terminal condition and quadratic growth in z.

Infinite convolutions of probability measures on Polish semigroups

This expository paper is intended for a short self-contained introduction to the theory of infinite convolutions of probability measures on Polish semigroups. We give the proofs of the Rees decomposition theorem of completely simple semigroups, the Ellis--Żelazko theorem, the convolution factorization theorem of convolution idempotents, and the convolution factorization theorem of cluster points of infinite convolutions.

A CLT for dependent random variables, with an application to an infinite system of interacting diffusion processes

We present a central limit theorem for stationary random fields that are short-range dependent and asymptotically independent. As an application, we present a central limit theorem for an infinite family of interacting Itô-type diffusion processes.

关于关于时间可无限整除的过程

On processes which are infinitely divisible with respect to time

这篇短文的目的是提出IDT过程的概念，IDT过程是从修改的无限可分性质得到的Lévy过程的广泛推广。特别注意的是把一些例子，以澄清有多少IDT过程要么不同，或类似于，Lévy过程。

Exact asymptotics in an infinite-server system with overdispersed input

This short communication considers an infinite-server system with overdispersed input. The objective is to identify the exact tail asymptotics of the number of customers present at a given point in time under a specific scaling of the model (which involves both the arrival rate and time). The proofs rely on a change-of-measure approach. The results obtained are illustrated by a series of examples.

Infinite Horizon Multi-Dimensional BSDE with Oblique Reflection and Switching Problem

This paper studies a system of multi-dimensional reflected backward stochastic differential equations with oblique reflections (RBSDEs for short) in infinite horizon associated to switching problems. The existence and uniqueness of the adapted solution is obtained by using a method based oa combination of penalization, verification method and contraction property.

Modelling and Differential Costs Evaluation of a Two Echelons Repair System through Infinite Servers Nodes Queuing Networks

After a short report of results on infinite servers queues systems, focusing on its busy period, using networks of queues with infinite servers nodes a model is constructed to study a two echelons repair system. These repair systems may be useful, for instance, in the operation of a fleet of aircraft, of shipping or of trucks. Additionally, it is shown how this model may be used in the evaluation of differential costs.

Levy测度的反演及Levy过程的长、短时性态之间的关系

Inversions of Levy Measures and the Relation Between Long and Short Time Behavior of Levy Processes

Levy测度的反演在Sato 2007年首次引入（以不同的名称）。我们推广了这个定义并给出了一些性质。然后，我们使用反演推导出之间的关系弱收敛的一个Levy过程的无穷方差稳定分布时，时间接近零时和弱收敛的一个不同的Levy过程的时间接近无穷大。这使我们能够得到自包含的条件，一个列维过程收敛到一个无穷方差稳定分布的时间接近零。我们制定我们的结果一般Levy过程和重要的一类回火稳定的Levy过程。对于后一类，我们给出了详细的结果，他们的Rosinski措施。

无限维扩散与耗尽相互作用：一种胶体模型的研究

Infinite-dimensional diffusions and depletion interaction for a model of colloids

该研究探讨了胶体模型中不同大小硬球的无限维扩散动力学，发现大球间短程吸引耗尽相互作用，并分析了相关Gibbs测度与渗流及最优排列的联系。