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In this paper, we study a notion of local stationarity for discrete time Markov chains which is useful for applications in statistics. In the spirit of some locally stationary processes introduced in the literature, we consider triangular…

Statistics Theory · Mathematics 2016-10-06 Lionel Truquet

The term noncentral moderate deviations is used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between the convergence in probability to a constant (governed by a reference large deviation…

Probability · Mathematics 2025-04-29 Neha Gupta , Claudio Macci

We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on convexity of the free energy along interpolations in a…

Probability · Mathematics 2020-06-04 Matthias Erbar , Max Fathi , André Schlichting

For Markov chains and Markov processes exhibiting a form of stochastic monotonicity (larger states shift up transition probabilities in terms of stochastic dominance), stability and ergodicity results can be obtained using order-theoretic…

Probability · Mathematics 2024-10-01 Takashi Kamihigashi , John Stachurski

The purpose of this paper is to estimate the limiting variance of asymptotically stationary Gaussian processes observed at high frequency, using the second moment estimator (SME). We study rates of convergence of the central limit theorem…

Probability · Mathematics 2026-03-06 Khalifa Es-Sebaiy , Yong Chen

It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…

Statistics Theory · Mathematics 2021-04-23 Graeme Auld , Ioannis Papastathopoulos

We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…

Probability · Mathematics 2017-03-24 Hanchao Wang , Zhengyan Lin , Zhonggen Su

Adaptive Markov chains are an important class of Monte Carlo methods for sampling from probability distributions. The time evolution of adaptive algorithms depends on past samples, and thus these algorithms are non-Markovian. Although there…

Probability · Mathematics 2014-10-02 Natesh S. Pillai , Aaron Smith

We extend previous large deviations results for the randomised Heston model to the case of moderate deviations. The proofs involve the G\"artner-Ellis theorem and sharp large deviations tools.

Pricing of Securities · Quantitative Finance 2020-05-06 Antoine Jacquier , Fangwei Shi

We prove Berry-Esseen theorems, almost sure invariance principle rates and large deviations for products of independent but not identically distributed invertible matrices with some average (logarithmic) projective contraction and uniform…

Probability · Mathematics 2025-12-23 Yeor Hafouta

This paper proves a Berry--Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be $O(n^{-1/2})$ as $n\to\infty$, where $n$ denotes the sample…

Probability · Mathematics 2009-03-02 S. N. Lahiri , S. Sun

We investigate a class of stochastic partial differential equations of reaction-diffusion type defined on graphs, which can be derived as the limit of SPDEs on narrow planar channels. In the first part, we demonstrate that this limit can be…

Probability · Mathematics 2024-03-21 Sandra Cerrai , Wen-Tai Hsu

By comparing the original equations with the corresponding stationary ones, the moderate deviation principle (MDP) is established for unbounded additive functionals of several different models of distribution dependent SDEs, with…

Probability · Mathematics 2021-01-26 Panpan Ren , Shen Wang

This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…

Probability · Mathematics 2013-05-06 Daniel Paulin , Lester Mackey , Joel A. Tropp

In this paper we investigate the speed of convergence of the fluctuations of a general class of Feynman-Kac particle approximation models. We design an original approach based on new Berry-Esseen type estimates for abstract martingale…

Probability · Mathematics 2007-05-23 Pierre Del Moral , Samy Tindel

We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of a strictly stationary orthomartingale random field. These inequalities can be used to establish complete convergence of…

Probability · Mathematics 2020-03-10 Davide Giraudo

In this paper, we derive Hybrid, Bayesian and Marginalized Cram\'{e}r-Rao lower bounds (HCRB, BCRB and MCRB) for the single and multiple measurement vector Sparse Bayesian Learning (SBL) problem of estimating compressible vectors and their…

Machine Learning · Computer Science 2015-06-04 Ranjitha Prasad , Chandra R. Murthy

We seek to characterize the estimation performance of a sensor network where the individual sensors exhibit the phenomenon of drift, i.e., a gradual change of the bias. Though estimation in the presence of random errors has been extensively…

Information Theory · Computer Science 2012-06-19 Swarnendu Kar , Pramod K. Varshney , Marimuthu Palaniswami

An exchangeable pair approach is commonly taken in the normal and non-normal approximation using Stein's method. It has been successfully used to identify the limiting distribution and provide an error of approximation. However, when the…

Probability · Mathematics 2021-04-28 Qi-Man Shao , Zhuo-Song Zhang

The purpose of this paper is twofold. In one direction, we extend the spectral method for random piecewise expanding and hyperbolic dynamics developed by the first author \textit{et al}. to establish quenched versions of the large deviation…

Dynamical Systems · Mathematics 2020-12-02 Davor Dragičević , Yeor Hafouta