Perturbations of copulas and Mixing properties

New copulas and their applications to symmetrizations of bivariate copulas

New copulas, based on perturbation theory, are introduced to clarify a \emph{symmetrization} procedure for asymmetric copulas. We give also some properties of the \emph{symmetrized} copula. Finally, we examine families of copulas with a prescribed symmetrized one. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.

Some Aspects of Modeling Dependence in Copula-based Markov chains

Dependence coefficients have been widely studied for Markov processes defined by a set of transition probabilities and an initial distribution. This work clarifies some aspects of the theory of dependence structure of Markov chains generated by copulas that are useful in time series econometrics and other applied fields. The main aim of this paper is to clarify the relationship between the notions of geometric ergodicity and geometric ρ-mixing; namely, to point out that for a large number of well known copulas, such as Clayton, Gumbel or Student, these notions are equivalent. Some of the resul…

指数混合Copulas

Index-mixed copulas

研究引入指数混合Copulas，由基础Copulas和随机指数向量构建，推导其解析形式与密度，给出采样算法，研究多种性质并应用，还解释了EFGM Copulas族，展现出解析易处理且不受限的特点。

带常数大小扰动的环上的混合

Mixing on the cycle with constant size perturbation

本文研究环上马尔可夫链，通过添加固定数量随机边并采用非可逆转移，将混合时间改进至近二次阶 $O(n^{\frac{k+2}{k+1}})$，基于有偏随机游走构造。

Random walk on a perturbation of the infinitely-fast mixing interchange process

We consider a random walk in dimension $d\geq 1$ in a dynamic random environment evolving as an interchange process with rate $γ>0$. We only assume that the annealed drift is non-zero. We prove that the empirical velocity of the walker $X_t/t$ eventually lies in an arbitrary small ball around the annealed drift if we choose $γ$ large enough. This statement is thus a perturbation of the case $γ=+\infty$ where the environment is refreshed between each step of the walker. We extend three-way part of the results of HS15, where the environment was given by the $1$ dimensional exclusion process: $(i…

Ergodicity and mixing for stochastic partial differential equations

Recently, a number of authors have investigated the conditions under which a stochastic perturbation acting on an infinite dimensional dynamical system, e.g. a partial differential equation, makes the system ergodic and mixing. In particular, one is interested in finding minimal and physically natural conditions on the nature of the stochastic perturbation. I shall review recent results on this question; in particular, I shall discuss the Navier-Stokes equation on a two dimensional torus with a random force which is white noise in time, and excites only a finite number of modes. The number of …

强空间混合条件下Gibbs采样器的二阶扰动界

Second-order perturbation bounds for Gibbs samplers under strong spatial mixing

本研究在强空间混合条件下，通过三种方法证明了Gibbs采样器扰动分析中的“平方根”现象，即一步误差约为$1/\sqrt{\tau}$时局部更新仍有效，并展示了其在MCMC算法调参中的应用。

On averaging and mixing for stochastic PDEs

We examine the convergence in the Krylov--Bogolyubov averaging for nonlinear stochastic perturbations of linear PDEs with pure imaginary spectrum and show that if the involved effective equation is mixing, then the convergence is uniform in time.

马尔可夫链在一般空间上具有无界随机环境的尖锐混合速率

Sharp Mixing Rates for Markov Chains on General Spaces with Unbounded Random Environments

本文研究了在一般空间上具有无界随机环境的马尔可夫链，证明了其收敛速率和强混合性，并在特定自回归过程中实现了最优混合速率。