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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements I: Large deviation principle of occupation measures
随机交错 大偏差 占用措施 大偏差原则
2023/5/10
In this lecture, I will talk about the large deviation problems in random interlacements, in particular the LDP of the occupation measure, and discuss its relations to sharp asymptotic probabilities o...
Distributed average consensus with least-mean-square deviation
Distributed average consensus Least-mean-square Convex optimization Edge-transitive graphs
2015/8/10
We consider a stochastic model for distributed average consensus, which arises in applications such as load balancing for parallel processors, distributed coordination of mobile autonomous agents, and...
The Sharp Lower Bound of Asymptotic Efficiency of Estimators in the Zone of Moderate Deviation Probabilities
The Sharp Lower Bound Asymptotic Efficiency of Estimators the Zone of Moderate Deviation Probabilities Statistics Theory
2012/6/27
For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower...
A moderate deviation principle for empirical bootstrap measure
Large deviations moderate deviations bootstrap empirical measure
2012/6/27
We establish two moderate deviation principles (MDP) in the bootstrap setting. We prove MDP for the joint distribution of the empirical measure and the empirical bootstrap measure (empirical measure o...
Control of the multiclass G/G/1 queue in the moderate deviation regime
Risk-sensitive control large deviations moderate deviations differential games multi-class single-server queue
2012/5/24
A multi-class single-server system with general service time distributions is studied in a moderate deviation heavy traffic regime. In the scaling limit, an optimal control problem associated with the...
Moderate Deviation Principle for dynamical systems with small random perturbation
Freidlin-Wentzell’s theorem large deviations moderate deviations Talagrand’s transportation inequality
2011/9/14
Abstract: Consider the stochastic differential equation in $\rr^d$
dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t
X^{\e}_0&=x_0,\quad x_0\in\rr^d
where $b:\rr^d\rightarrow\rr^d$ is $C^1$ s...
Large Deviation Theory for a Homogenized and "Corrected" Elliptic ODE
Differential equations probability theory random coefficients
2011/1/18
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 ...
Non-asymptotic deviation inequalities for smoothed additive functionals in non-linear state-space models with applications to parameter estimation
Non-asymptotic deviation inequalities smoothed additive functionals in non-linear state-space parameter estimation
2011/2/22
Approximating joint smoothing distributions using particle-based methods is a well-known issue in statistical inference when operating on general state space hidden Markov models (HMM). In this paper ...
Inviscid Large deviation principle and the 2D Navier Stokes equations with a free boundary condition
Inviscid Large deviation principle the 2D Navier Stokes equations
2010/11/23
Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root ...
Interpolating Thin-Shell and Sharp Large-Deviation Estimates For Isotropic Log-Concave Measures
Interpolating Thin-Shell Sharp Large-Deviation Estimates Isotropic Log-Concave Measures
2010/11/9
Given an isotropic random vector $X$ with log-concave density in Euclidean space $\Real^n$, we study the concentration properties of $|X|$. We show in particular that: \[ \P(|X| \geq (1+t) \sqrt{n}) ...
Large deviation principles for non gradient weakly asymmetric stochastic lattice gases
deviation principles gradient weakly lattice gases
2010/11/11
We consider a lattice gas on the discrete d-dimensional torus (Z/NZ)^d with a generic translation invariant, finite range interaction satisfying a uniform strong mixing condition. The lattice gas perf...
Large deviation properties of weakly interacting processes via weak convergence methods
Large deviation properties weakly interacting processes weak convergence methods
2010/12/14
We study large deviation properties of systems of weakly interacting particles modeled by Itô stochastic differential equations (SDEs).It is known under certain conditions that the corresponding...
Large deviation results for Multitype Galton-Watson trees
Tree-indexed Markov chain Tree-indexed process random tree
2010/12/7
Using the notion of consistency of empirical measures, under fairly general assumption we
prove a joint large deviation principles in n for the empirical pair measure and empirical
offspring measure...
Challenging the empirical mean and empirical variance: a deviation study
Non-parametric estimation M-estimators PAC-Bayes bounds
2010/12/3
We present new M-estimators of the mean and variance of real valued random variables, based on PAC-Bayes bounds. We analyze the non-asymptotic minimax properties of the deviations of those estimators ...
Least Deviation Decomposition with Respect to a Pair of Convex Sets
Least deviation decomposition convex analysis Moreau orthogonal decomposition
2009/1/20
Let $K_1$ and $K_2$ be two nonempty closed convex sets in some normed space $(H,\Vert \cdot \Vert )$. This paper is concerned with the question of finding a "good" decomposition, with respect to $K_1$...