我们提出了大偏差估计的上确界范数的系统的独立随机游动叠加的出生和死亡的动态发展的离散环面$N$网站。所考虑的标度极限是所谓的\textit{high density limit}（参见对该主题的调查\cite{franco}），其中空间，时间和粒子的初始数量被重新标度。这里得到的相关速率泛函是\cite{JonaLandimVares}的速率函数的半线性化版本，它处理了与生灭动力学叠加的排斥过程的大偏差。证明大偏差的一个要素在于提供一个适当的原始过程扰动类的极限。这正是这项工作的主要贡献之一：一种将原始高密度方法（如\cite{Arnold,blount2,blount,francogroisman,Kote2,KoteHigh1988}）扩展到弱非对称系统的策略。两种情况被认为是相对于粒子的初始数量，幂律和（至少）指数增长性。在第一种情况下，我们提出的下界只在一定的子集上的光滑的配置文件，而在第二种情况下，另外假设的出生和死亡的功能和一个恒定的初始配置文件，我们提供了一个完整的大偏差原则。
英文摘要：
We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called \textit{high density limit} (see the survey \cite{franco} on the subject), where space, time and initial quantity of particles are rescaled. The associated rate functional here obtained is a semi-linearised version of the rate function of \cite{JonaLandimVares}, which dealt with large deviations of exclusion processes superposed with birth-and-death dynamics. An ingredient in the proof of large deviations consists in providing a limit of a suitable class of perturbations of the original process. This is precisely one of the main contributions of this work: a strategy to extend the original high density approach (as in \cite{Arnold,blount2,blount,francogroisman,Kote2,KoteHigh1988}) to weakly asymmetric systems. Two cases are considered with respect to the initial quantity of particles, the power law and the (at least) exponential growth. In the first case, we present the lower bound only on a certain subset of smooth profiles, while in the second case, additionally assuming concavity of the birth and the death functions and a constant initial profile, we provide a full large deviations principle.
A large deviation principle in Hölder norm for multiple fractional integrals
对于具有Hurst参数$H\in]{1/4},{1/2}[\cup]{1/2},1[$的分数布朗运动$B^H$，构造了单形上的多重不定积分，并研究了其样本路径的正则性.然后证明了用$ε^{1/2} B^H$代替$B^H$得到的过程的概率律族在Hölder范数下满足大偏差原理.多重积分的定义依赖于分数布朗运动关于标准布朗运动的随机积分的表示。对于大偏差原理，Ledoux在[Lecture Notes in Math.，Vol.1426（1990）1-14]。
