随机场的非传统不变原理

Invariance principles for clocks

We show an invariance principle for rescaled clocks of positive semi-stable Markov processes, proving a conjecture presented in Remark 4 in Demni, Rouault, Zani [11], 2015.

随机电导模型淬火与退火不变原理的比较：II部分

Comparison of quenched and annealed invariance principles for random conductance model: Part II

我们发现，存在一个遍历电导环境，使弱（退火）不变原理保持相应的连续时间随机游动，但淬火不变原理不成立。本文给出了弱不变原理的满标度极限的一个证明，改进了文[1]中得到的一个连续极限的结果。

一类马尔可夫链重对数律的不变原理

An invariance principle for the law of the iterated logarithm for some Markov chains

证明了在Wasserstein度量下具有谱间隙的马尔可夫链的可加泛函的Strassen不变原理.

一类带乘性随机源的反应扩散方程的不变性原理

An Invariance Principle for some Reaction-Diffusion Equations with a Multiplicative Random Source

本文通过建立抛物型随机偏微分方程的不变性原理确立了抛物型安德森模型的普适性，并利用该原理为非线性随机偏微分方程提供渐近理论，其新要素为底层方程的耗散性。

Invariance principles for random walks in cones

We prove invariance principles for a mulditimensional random walk conditioned to stay in a cone. Our first result concerns convergence towards the Brownian meander in the cone. Furthermore, we prove functional convergence of $h$-transformed random walk to the corresponding $h$-transform of the Brownian motion. Finally, we prove an invariance principle for bridges of a random walk in a cone.

Almost sure invariance principle for the Kantorovich distance between the empirical and the marginal distributions of strong mixing sequences

We prove a strong invariance principle for the Kantorovich distance between the empiricaldistribution and the marginal distribution of stationary $α$-mixing sequences.

标准规范化和自规范化随机场的不变原理

Invariance principles for standard-normalized and self-normalized random fields

研究了鞅差平稳域$(X\_{k})\_{k\in\mathbb{Z}^{d}}$和独立随机变量的集指标部分和分别在标准正规化和自正规化下的不变原理.

The invariance principle and the large deviation for the biased random walk on $\mathbb{Z}^d$

In this paper, we establish the invariance principle and the large deviation for the biased random walk $RW_λ$ with $λ\in [0,1)$ on $\mathbb{Z}^d, d\geq 1$.

平稳过程的猝灭不变原理

A quenched invariance principle for stationary processes

本文证明了在Hannan条件下，平稳过程的猝灭弱不变原理的条件中心形式。在这个过程中，我们得到了一个（新的）结构的事实，即任何平稳过程可以看作是一个功能的马尔可夫链。

H{ö}lderian weak invariance principle under Maxwell and Woodroofe condition

We investigate the weak invariance principle in H{ö}lder spaces under some reinforcement of the Maxwell and Woodroofe condition.

Weak invariance principle in Besov spaces for stationary martingale differences

The classical Donsker weak invariance principle is extended to a Besov spaces framework. Polygonal line processes build from partial sums of stationary martingale differences as well independent and identically distributed random variables are considered. The results obtained are shown to be optimal.

马尔可夫链可加泛函重对数律的一个不变原理

An invariance principle for the law of the iterated logarithm for additive functionals of Markov chains

本文利用鞅论和分式上边界理论证明了马尔可夫链的向量值可加泛函的Strassen强不变原理。这个假设是一个约束在预解式上的矩。

具有随机电导的随机游动的猝灭不变原理

Quenched invariance principles for random walks with random conductances

证明了独立同分布随机游动的一个几乎必然不变原理。以$\Z^d$、$d\geq 2$为单位的电导。我们假设电导是从上面有界的，但我们不要求它们是从下面有界的。

关于随机变量和乘积的不变原理的一个注记

A note on the invariance principle of the product of sums of random variables

文献中研究了各种随机变量和乘积的中心极限定理。本文旨在说明这类结果是不变原理的推论。

Holderian weak invariance principle under a Hannan type condition

We investigate the invariance principle in H{ö}lder spaces for strictly stationary martingale difference sequences. In particular, we show that the sufficient condition on the tail in the i.i.d. case does not extend to stationary ergodic martingale differences. We provide a sufficient condition on the conditional variance which guarantee the invariance principle in H{ö}lder spaces. We then deduce a condition in the spirit of Hannan one.

连续渗流簇中反射扩散的淬火不变性原理

Quenched Invariance Principle for a Reflecting Diffusion in a Continuum Percolation Cluster

本文研究了平稳遍历点过程上的连续渗流，在占据区域存在唯一无界簇且满足体积正则性和等周条件的假设下，证明了簇上反射扩散的淬火不变性原理。

随机场景中布朗运动的一个不变原理

An invariance principle for Brownian motion in random scenery

本文用特征函数的方法证明了高斯或泊松随机场景中布朗运动的一个不变原理。退火的渐近极限推导出在所有的维度，重点放在尺寸$d=2$，这是主要的新贡献的文件的情况下。

Donsker's invariance principle under the sub-linear expectation with an application to Chung's law of the iterated logarithm

We prove a new Donsker's invariance principle for independent and identically distributed random variables under the sub-linear expectation. As applications, the small deviations and Chung's law of the iterated logarithm are obtained.

马尔可夫链可加泛函的几乎必然不变原理

An Almost Sure Invariance Principle for Additive Functionals of Markov Chains

证明了马尔可夫链的向量值可加泛函关于遍历平衡分布对几乎所有起点的不变原理（泛函中心极限定理）。这个假设是一个约束在预解式上的矩。

短记忆随机过程的不变原理

Invariance principle for stochastic processes with short memory

本文给出了短记忆线性过程蕴含不变原理的简单充分条件。各种例子，包括投影准则被认为是应用。特别地，我们讨论了短记忆线性过程部分和的弱不变原理。证明了只要新息的部分和满足$L_p$ --不变原理，则相应的线性过程的部分和也满足$L_p$ --不变性原理。

Holderian weak invariance principle for stationary mixing sequences

We provide some sufficient mixing conditions on a strictly stationary sequence in order to guarantee the weak invariance principle in Hölder spaces. Strong mixing and $ρ$-mixing conditions are investigated as well as $τ$-dependent sequences. The main tools are Fuk-Nagaev type inequalities for mixing sequences and a truncation argument.

A strictly stationary $β$-mixing process satisfying the central limit theorem but not the weak invariance principle

In 1983, N. Herrndorf proved that for a $ϕ$-mixing sequence satisfying the central limit theorem and $\liminf_{n\to\infty}\frac{σ^2_n}n>0$, the weak invariance principle takes place. The question whether for strictly stationary sequences with finite second moments and a weaker type ($α$, $β$, $ρ$) of mixing the central limit theorem implies the weak invariance principle remained open. We construct a strictly stationary $β$-mixing sequence with finite moments of any order and linear variance for which the central limit theorem takes place but not the weak invariance principle.

Quenched invariance principle for random walks on Delaunay triangulations

We consider simple random walks on Delaunay triangulations generated by point processes in $\mathbb{R}^d$. Under suitable assumptions on the point processes, we show that the random walk satisfies an almost sure (or quenched) invariance principle. This invariance principle holds for point processes which have clustering or repulsiveness properties including Poisson point processes, Mat{é}rn cluster and Mat{é}rn hardcore processes. The method relies on the decomposition of the process into a martingale part and a corrector which is proved to be negligible at the diffusive scale.

On the invariance principle for empirical processes of associated sequences

We consider empirical processes generated by strictly stationary sequences of associated random variables. S. Louhichi established an invariance principle for such processes, assuming that the covariance function decays rapidly enough. We show that under certain conditions imposed on the pairwise distributions of the random variables in question the restrictions on the rate of decay of the covariance function can be relaxed.

分数布朗单的一个不变原理

An invariance principle for fractional Brownian sheets

建立了具有相依新息的平稳线性随机场部分和的中心极限定理和各向异性分数布朗单的不变原理。我们的结果是Dedecker等人（2011）的分数布朗运动的不变原理在高维的推广。他们的论点的一个关键组成部分，鞅近似，被替换为m-近似参数。我们的方法的一个重要工具是最近由El Machkouri et al.（2011）建立的平稳随机场的矩不等式。

Total variation distance between stochastic polynomials and invariance principles

The goal of this paper is to estimate the total variation distance between two general stochastic polynomials. As a consequence one obtains an invariance principle for such polynomials. This generalizes known results concerning the total variation distance between two multiple stochastic integrals on one hand, and invariance principles in Kolmogorov distance for multi-linear stochastic polynomials on the other hand. As an application we first discuss the asymptotic behavior of U-statistics associated to polynomial kernels. Moreover we also give an example of CLT associated to quadratic forms.

非适应序列强不变原理的收敛速度。环面遍历自同构的应用

Rates of convergence in the strong invariance principle for non adapted sequences. Application to ergodic automorphisms of the torus

本文给出了满足投影准则的非适应序列的强不变原理的收敛速度。结果适用于遍历自同构T的d维环面的迭代，即使在非双曲的情况下。在本文中，我们给出了一个从d维环面到R的无界函数f的大类，其中f的部分和foT+ foT^2 +. + foT^n满足一个强不变原理，并具有显式的收敛速率。

渗流簇上随机游动的猝灭不变原理

Quenched invariance principles for random walks on percolation clusters

证明了$\Z^d$中无限Bernoulli渗流簇上随机游动的几乎必然（“猝灭”）不变原理，其中$d$大于或等于2.

Invariance principle for random walks on dynamically averaging random conductances

We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb Z$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations decrease according to a typical diffusive scaling and eventually approach constant unit conductances. The proof relies on a coupling with the standard continuous time simple random walk.

Invariance principle for the maximal position process of branching Brownian motion in random environment

In this paper we study the maximal position process of branching Brownian motion in random spatial environment. The random environment is given by a process $ξ= \left(ξ(x)\right)_{x\in\mathbb{R}}$ satisfying certain conditions. We show that the maximum position $M_t$ of particles alive at time $t$ satisfies a quenched strong law of large numbers and an annealed invariance principle.

Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment

We study the asymptotic behaviour of random walks in i.i.d. non-elliptic random environments on $\mathbb{Z}^d$. Standard conditions (and proofs) for ballisticity and the central limit theorem require ellipticity. We use oriented percolation and martingale arguments to give non-trivial local conditions for ballisticity and an annealed invariance principle in the non-elliptic setting.

非周期随机游走：一致估计、局部极限与不变原理

Aperiodic random walks: uniform estimates, local limits and invariance principles

本文针对带一致指数尾的非周期整数值随机游走三角阵列，证明了一致端点估计、局部极限与条件桥不变原理，其增量律可随尺度参数变化，端点估计覆盖所有非负高度。

平稳序列不变原理的新进展

Recent advances in invariance principles for stationary sequences

本文综述了平稳序列的中心极限定理及其弱不变原理的一些最新结果。我们还描述了几个极大不等式，它们是获得不变原理的主要工具，而且它们本身也很有趣。所考虑的相依随机变量类有类鞅序列、混合序列、线性过程、遍历马尔可夫链的可加泛函。

非齐次丢番图逼近的不变性原理

The invariance principle for inhomogeneous Diophantine approximations

本文利用累积量方法，通过仿射格点空间上高阶相关性的有效混合，证明了非齐次丢番图逼近的中心极限定理与不变性原理。

Symmetric exclusion as a random environment: invariance principle

We establish an invariance principle for a one-dimensional random walk in a dynamical random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite box around the walker. The environment starts from equilibrium. After a suitable space-time rescaling, the random walk converges to a sum of two independent processes, a Brownian motion and a Gaussian process with stationary increments.

An invariance principle for the two-dimensional parabolic Anderson model with small potential

We prove an invariance principle for the two-dimensional lattice parabolic Anderson model with small potential. As applications we deduce a Donsker type convergence result for a discrete random polymer measure, as well as a universality result for the spectrum of discrete random Schrödinger operators on large boxes with small potentials. Our proof is based on paracontrolled distributions and some basic results for multiple stochastic integrals of discrete martingales.

随机环境中随机游动的Strassen不变原理

Strassen's invariance principle for random walk in random environment

本文考虑了$\mathbb{Z}^{d}\,(d\geq1)$上随机环境中的随机游动，利用鞅论和Derriennic和Lin \cite{DL}的分数余边界理论，在一定条件下证明了该模型的Strassen强不变原理.所得结果部分地填补了大数定律与中心极限定理之间的空白。

Deviation inequalities for martingales with applications to linear regressions and weak invariance principles

Using changes of probability measure developed by \mbox{Grama} and Haeusler (Stochastic Process.\ Appl., 2000), we obtain two generalizations of the deviation inequalities of Lanzinger and Stadtmüller (Stochastic Process.\ Appl., 2000) and Fuk and Nagaev (Theory Probab. Appl., 1971) to the case of martingales. Our inequalities recover the best possible decaying rate of independent case. Applications to linear regressions and weak invariance principles for martingales are provided.

动态有界随机电导模型的不变原理

Invariance Principle for the Random Conductance Model with dynamic bounded Conductances

研究了动态随机电导环境中的连续时间随机游动X。我们假设电导是平稳遍历的，一致有界的，有界远离零和多项式混合的空间和时间。证明了X的猝灭不变原理，得到了格林函数的界和局部极限定理.我们还讨论了随机接口模型的连接。

相依随机变量的强不变原理

Strong invariance principles for dependent random variables

建立了平稳过程和遍历过程和的强不变原理，并给出了它们的近似最优界。线性和一些非线性过程的应用进行了讨论。强大数定律和重对数定律也得到了易于验证的条件下。

Quenched invariance principle for random walk in time-dependent balanced random environment

We prove a quenched central limit theorem for balanced random walks in time dependent ergodic random environments which is not necessarily nearest-neigbhor. We assume that the environment satisfies appropriate ergodicity and ellipticity conditions. The proof is based on the use of a maximum principle for parabolic difference operators.

Invariance principles for integrated random walks conditioned to stay positive

Let $S(n)$ be a centered random walk with finite second moment. We consider the integrated random walk $T(n) = S(0)+S(1)+\dots+S(n)$. We prove invariance principles for the meander and for the bridge of this process, under the condition that the integrated random walk remains positive. Furthermore, we prove the functional convergence of its Doob's $h$-transform to the $h$-transform of the Kolmogorov diffusion conditioned to stay positive.

“逆”鞅的速率强不变原理及其应用

Strong invariance principles with rate for "reverse" martingales and applications

本文得到了关于逆鞅差序列和的具有$n^{1/p}\log^βn$、$2< p\le 4$阶速率的几乎必然不变原理.然后，我们将这些结果应用到一些不可逆动力系统的背景下，得到类似的结论。例如，我们对待几个类的一致扩展映射的区间（可能无界的功能）。在课程中得到了$ϕ$依赖序列的一般结果。

独立同分布中某些弹道随机游动的猝灭不变原理。环境

A quenched invariance principle for certain ballistic random walks in i.i.d. environments

证明了独立同分布中的每个随机游动。在维数大于或等于2的环境中，在某个方向上具有几乎必然的正速度，退火不变原理和再生次数的一些温和的可积性条件也满足淬火不变原理。该论点是基于交叉估计和定理Bolthausen和Sznitman。

动态随机环境中连续空间随机游动的几乎必然不变原理

Almost Sure Invariance Principle for Continuous-Space Random Walk in Dynamic Random Environment

我们考虑了在多项式混合随机环境中$\R^d$上的随机游动，该环境在每个时间步都被刷新。利用鞅方法给出了几乎处处泛函中心极限定理成立的一个充要条件。

The principle of invariance in the Donsker form to the partial sum processes of finite order moving averages

We consider the process of partial sums of moving averages of finite order with a regular varying memory function, constructed from a stationary sequence, variance of the sum of which is a regularly varying function. We study the Gaussian approximation of this process of partial sums with the aid of a certain class of Gaussian processes, and obtain sufficient conditions for the $C$-convergence in the invariance principle in the Donsker form

电导无界的随机电导模型的不变原理

Invariance principle for the random conductance model with unbounded conductances

研究了在独立同分布环境下的连续时间随机游动$X$.随机电导$μ_e\in[1,\infty)$。我们得到了热核的界，并证明了一个淬火不变原理的$X$。即使当${\mathbb{E}}μ_e=\infty$ .

Invariance principle via orthomartingale approximation

We obtain a necessary and sufficient condition for the orthomartingale-coboundary decomposition. We establish a sufficient condition for the approximation of the partial sums of a strictly stationary random fields by those of stationary orthomartingale differences. This condition can be checked under multidimensional analogues of the Hannan condition and the Maxwell-Woodroofe condition.

Invariance principles for local times in regenerative settings

Consider a stochastic process $\mathfrak{X}$, regenerative at a state $x$ which is instantaneous and regular. Let $L$ be a regenerative local time for $\mathfrak{X}$ at $x$. Suppose furthermore that $\mathfrak{X}$ can be approximated by discrete time regenerative processes $\mathfrak{X}^n$ for which $x$ is accesible. We give conditions on $\mathfrak{X}$ and $\mathfrak{X}^n$ so that the naturally defined local time of $\mathfrak{X}^n$ converges weakly to $L$. This limit theorem generalizes previous invariance principles that have appeared in the literature.

具有禁止方向的多维弹道随机游动的猝灭不变原理

Quenched invariance principle for multidimensional ballistic random walk in a random environment with a forbidden direction

我们考虑独立同分布中的弹道随机游动。不允许向某个固定方向撤退的随机环境。我们证明了一个不变原理（泛函中心极限定理），几乎在每一个固定的环境。假设是nonnestling，至少两个空间维度，和$2+ε$时刻的步行步骤均匀的环境。不变原理背后的要点是，游走的猝灭平均值表现为亚扩散。

Almost sure invariance principle of $β-$mixing time series in Hilbert space

Inspired by \citet{Berkes14} and \citet{Wu07}, we prove an almost sure invariance principle for stationary $β-$mixing stochastic processes defined on Hilbert space. Our result can be applied to Markov chain satisfying Meyn-Tweedie type Lyapunov condition and thus generalises the contraction condition in \citet[Example 2.2]{Berkes14}. We prove our main theorem by the big and small blocks technique and an embedding result in \citet{gotze2011estimates}. Our result is further applied to the ergodic Markov chain and functional autoregressive processes.

Invariance Principles for Tempered Fractionally Integrated Processes

We discuss invariance principles for autoregressive tempered fractionally integrated moving averages in $α$-stable $(1< α\le 2)$ i.i.d. innovations and related tempered linear processes with vanishing tempering parameter $λ\sim λ_*/N$. We show that the limit of the partial sums process takes a different form in the weakly tempered ($λ_* = 0$), strongly tempered ($λ_* = \infty$), and moderately tempered ($0<λ_* < \infty$) cases. These results are used to derive the limit distribution of the OLS estimate of AR(1) unit root with weakly, strongly, and moderately tempered moving average errors.

Invariance principles for random sums of random variables

This note investigates invariance principles for sums of N(nt) iid radom variables, where n is an integer, t is a positive real number and N(u) is a stochastic process with nonnegative integer values. We show that the sequence of sums of these random variables denoted S(n,t), when appropriately centered and normalized, weakly converges to a Gaussian process. We give sufficient conditions depending on the expectation of N(nt) which allows to rescale S(n,t) into a stochastic S(n,a(t)) weakly converging to a Brownian motion.

Invariance Principle for symmetric Diffusions in a degenerate and unbounded stationary and ergodic Random Medium

We study a symmetric diffusion $X$ on $\mathbb{R}^d$ in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients $a^ω$. The diffusion is formally associated with $L^ωu = \nabla\cdot(a^ω\nabla u)$, and we make sense of it through Dirichlet forms theory. We prove for $X$ a quenched invariance principle, under some moment conditions on the environment; the key tool is the sublinearity of the corrector obtained by Moser's iteration scheme.