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Introduction to Large Deviation Theory

open access: yes, 2014
This chapter provides an introduction to large deviation theory. It begins with an overview of the motivatio n for the problem under study, focusing on probability distributions and how to construct an empirical distribution. It then considers the notion of a lower semi-continuous function and that of a lower semi-continuous relaxation before ...
M. Vidyasagar
core   +3 more sources

Large Deviation Theory

Springer Series in Statistics, 2004
We will find that many of the rare events that we wish to simulate are the result of the occurrence of a large deviation event. In order to develop good simulation strategies for these events, we need to understand something of the probability theory associated with them.
James Antonio Bucklew
exaly   +2 more sources

Asymptotic Theory of Large Deviations for Markov Chains

SIAM Journal on Applied Mathematics, 1998
Let \(p_n(x,y)\) denote the density function of a real-valued stationary ergodic Markov chain \(X_n\) and its sample averages \(Y_n:={1\over n}\sum_{k=1}^n X_k\), i.e., \(p_n(x,y) dx dy=P(X_n\in dx, Y_n\in dy)\). This paper deals with the formal asymptotic expansion \[ p_n(x,y)=e^{-n\psi(n)}\sqrt{n} \Big[q^0(x,y)+ {q^1(x,y)\over n}+{q^2(x,y)\over n^2}+\
Gilad Lerman, Zeev Schuss
openaire   +3 more sources

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