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• Large Deviation Theory
"... Outline of the short course • Part 1: Information theory in a nutshell • Part 2: The method of types and its relationship with statistics ..."
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Outline of the short course • Part 1: Information theory in a nutshell • Part 2: The method of types and its relationship with statistics
Magnetic elements at finite temperature and large deviation theory
 J. Nonlinear Sci
"... Communicated by C. R. Doering Summary. We investigate thermally activated phenomena in micromagnetics using large deviation theory and concepts from stochastic resonance. We give a natural mathematical definition of finitetemperature astroids, finitetemperature hysteresis loops, etc. Generically, ..."
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Cited by 11 (3 self)
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Communicated by C. R. Doering Summary. We investigate thermally activated phenomena in micromagnetics using large deviation theory and concepts from stochastic resonance. We give a natural mathematical definition of finitetemperature astroids, finitetemperature hysteresis loops, etc. Generically
Large Deviation Theory for Stochastic Difference Equations
, 1997
"... The probability density for the solution yn of a stochastic di erence equation is considered. Following Knessl, Matkowsky, Schuss, and Tier [1] it is shown to satisfy a master equation, which is solved asymptotically for large values of the index n. The method is illustrated by deriving the large de ..."
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deviation results for a sum of independent identically distributed random variables and for the joint density of two dependent sums. Then it is applied to a difference approximation to the Helmholtz equation in a random medium. A large deviation result is obtained for the probability density of the decay
Large deviation theory for a homogenized and corrected elliptic
 ODE, J. Differential Equ
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2012) A basic introduction to large deviations: Theory, applications, simulations
"... The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic system is observed, the amplitude of the noise perturbing a d ..."
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Cited by 2 (0 self)
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The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic system is observed, the amplitude of the noise perturbing a
Application of large deviation theory to the meanfield ϕ 4model
, 2005
"... A large deviation technique is used to calculate the microcanonical entropy function s(v,m) of the meanfield ϕ 4model as a function of the potential energy v and the magnetization m. As in the canonical ensemble, a continuous phase transition is found. An analytical expression is obtained for the ..."
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A large deviation technique is used to calculate the microcanonical entropy function s(v,m) of the meanfield ϕ 4model as a function of the potential energy v and the magnetization m. As in the canonical ensemble, a continuous phase transition is found. An analytical expression is obtained
Large Deviations Theory, WeakNoise Asymptotics, And FirstPassage Problems: Review And Results
"... This paper addresses the effects of random perturbations on the longterm behavior of dynamical systems. Large excursions, escape from attractors and the corresponding (firstpassage) time scales are predicted probabilistically by two consistent asymptotic theories, the Theory of Large Deviations an ..."
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This paper addresses the effects of random perturbations on the longterm behavior of dynamical systems. Large excursions, escape from attractors and the corresponding (firstpassage) time scales are predicted probabilistically by two consistent asymptotic theories, the Theory of Large Deviations
2 Classical Large Deviation Theory Exponential Tilting: Let Sn = X1 + · · · + Xn and Xn = Sn/n. Since
"... Let Sn be a random walk formed by summing i.i.d. integer valued random variables Xi, i ≥ 1: Sn = X1 + · · · + Xn. If the drift EXi is negative, then Sn → − ∞ as n → ∞. If An is the event that Sk ≥ 0 for k = 1,..., n, then P (An) → 0 as n → ∞. In this talk we will consider conditional distribution ..."
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Let Sn be a random walk formed by summing i.i.d. integer valued random variables Xi, i ≥ 1: Sn = X1 + · · · + Xn. If the drift EXi is negative, then Sn → − ∞ as n → ∞. If An is the event that Sk ≥ 0 for k = 1,..., n, then P (An) → 0 as n → ∞. In this talk we will consider conditional distributions for the random walk given An. The main result will show that finite dimensional distributions for the random walk given An converge to those for a time homogeneous Markov chain on {0, 1,...}.
1A Survey on DelayAware Resource Control for Wireless Systems — Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning
, 2011
"... In this tutorial paper, a comprehensive survey is given on several major systematic approaches in dealing with delayaware control problems, namely the equivalent rate constraint approach, the Lyapunov stability drift approach and the approximate Markov Decision Process (MDP) approach using stochast ..."
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are elaborated. Finally, the delay performance of the various approaches are compared through simulations using an example of the uplink OFDMA systems. Index Terms Delayaware resource control, large deviation theory, Lyapunov stability, Markov decision process, stochastic learning.
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