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In 2013 A.A. Borovkov and A.A. Mogulskii proved a weaker-than-standard "metric" large deviations principle (LDP) for trajectories of random walks in $R^d$ whose increments have the Laplace transform finite in a neighbourhood of zero. We…

Probability · Mathematics 2021-04-05 Vladislav Vysotsky

In this paper, we study the non-asymptotic and asymptotic performances of the optimal robust policy and value function of robust Markov Decision Processes(MDPs), where the optimal robust policy and value function are solved only from a…

Machine Learning · Statistics 2022-08-16 Wenhao Yang , Liangyu Zhang , Zhihua Zhang

Let $(a_k)_{k\in\mathbb N}$ be a sequence of integers satisfying the Hadamard gap condition $a_{k+1}/a_k>q>1$ for all $k\in\mathbb N$, and let $$ S_n(\omega) = \sum_{k=1}^n\cos(2\pi a_k \omega),\qquad n\in\mathbb N,\;\omega\in [0,1]. $$ The…

Probability · Mathematics 2020-12-11 Christoph Aistleitner , Nina Gantert , Zakhar Kabluchko , Joscha Prochno , Kavita Ramanan

We prove a large deviation principle for the point process associated to $k$-element connected components in $\mathbb R^d$ with respect to the connectivity radii $r_n\to\infty$. The random points are generated from a homogeneous Poisson…

Probability · Mathematics 2022-10-19 Christian Hirsch , Takashi Owada

We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP does not require strict self-similarity assumptions on the Volterra…

Mathematical Finance · Quantitative Finance 2023-11-14 Giacomo Giorgio , Barbara Pacchiarotti , Paolo Pigato

In this paper we study empirical measures which can be thought as a decoupled version of the empirical measures generated by random matrices. We prove the large deviation principle with the rate function, which is finite only on product…

Probability · Mathematics 2007-05-23 Wlodek Bryc

We consider the quasi-deterministic behavior of systems with a large number, $n$, of deterministically interacting constituents. This work extends the results of a previous paper [J. Stat. Phys. 99:1225-1249 (2000)] to include vector-valued…

Statistical Mechanics · Physics 2021-04-28 Brian R. La Cour , William C. Schieve

In this paper, we first investigate the estimation of the empirical joint Laplace transform of volatilities of two semi-martingales within a fixed time interval [0, T] by using overlapped increments of high-frequency data. The proposed…

Statistics Theory · Mathematics 2025-03-05 XinWei Feng , Yu Jiang , Zhi Liu , Zhe Meng

Let $Z=\{Z(t): t\in \mathbb R\}$ be a stochastic process with trajectories in space $\mathbb D (\mathbb R)$. It is assumed that there exists an essentially smooth function $A:\mathbb R\to (-\infty, \infty] $ such that, for all $\alpha \in…

Probability · Mathematics 2026-05-01 A. A. Borovkov , K. A. Borovkov

We investigate large deviations for a family of conservative stochastic PDEs (conservation laws) in the asymptotic of jointly vanishing noise and viscosity. We obtain a first large deviations principle in a space of Young measures. The…

Probability · Mathematics 2009-04-06 Mauro Mariani

We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a "pointwise" large deviation principle (LDP) for the full…

Analysis of PDEs · Mathematics 2010-12-07 Guillaume Bal , Roger Ghanem , Ian Langmore

Stochastic domains often involve risk-averse decision makers. While recent work has focused on how to model risk in Markov decision processes using risk measures, it has not addressed the problem of solving large risk-averse formulations.…

Portfolio Management · Quantitative Finance 2012-10-19 Marek Petrik , Dharmashankar Subramanian

Given a sequence of Borel probability measures on a Hausdorff space which satisfy a large deviation principle, we consider the corresponding sequence of measures formed by conditioning on a set $B$. If the large deviation rate function $I$…

Probability · Mathematics 2021-04-27 Brian R. La Cour , William C. Schieve

Identification-robust hypothesis tests are commonly based on the continuous updating GMM objective function. When the number of moment conditions grows proportionally with the sample size, the large-dimensional weighting matrix prohibits…

Econometrics · Economics 2025-10-10 Tom Boot , Johannes W. Ligtenberg

The incidence of rare events in fast-slow systems is investigated via analysis of the large deviation principle (LDP) that characterizes the likelihood and pathway of large fluctuations of the slow variables away from their mean behavior --…

Statistical Mechanics · Physics 2016-02-17 Freddy Bouchet , Tobias Grafke , Tomás Tangarife , Eric Vanden-Eijnden

We consider the Markovian supermarket model with growing choices, where jobs arrive at rate $n\lambda_n$ and each of $n$ parallel servers processes jobs in its queue at rate $1$. Each incoming job joins the shortest among $d_n \in…

Probability · Mathematics 2025-08-13 Amarjit Budhiraja , Ruoyu Wu

We study the large deviation behavior of a system of diffusing particles with a mean field interaction, described through a collection of stochastic differential equations, in which each particle is driven by a vanishing independent…

Probability · Mathematics 2021-08-10 Amarjit Budhiraja , Michael Conroy

We prove large deviation principles (LDPs) for random matrices in the orthogonal group and Stiefel manifold, determining both the speed and good convex rate functions that are explicitly given in terms of certain log-determinants of…

Probability · Mathematics 2022-11-04 Zakhar Kabluchko , Joscha Prochno

The Large Deviation Principle (LDP) and the Central Limit Theorem (CLT) are central pillars of probability theory. While their formulations are established under the i.i.d. assumption, the probabilistic foundation for power-law…

Probability · Mathematics 2026-04-22 Hiroki Suyari , Antonio M. Scarfone

This article discusses modelling of the tail of a multivariate distribution function by means of a large deviation principle (LDP), and its application to the estimation of the probability of a multivariate extreme event from a sample of n…

Statistics Theory · Mathematics 2017-02-23 Cees de Valk