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Stochastic Modelling and Applied Probability
Apr 4, 2013 ... in general situations. To emphasize this point, derivations for many of the large deviations theorems using this approach have been provided. A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications,. Stochastic Modelling and Applied Probability 38,. DOI 10.1007/978-3-642-03311-7 1,.
Stochastic Modelling and Applied Probability
2005). 37 Yin, Continuous-Time Markov Chains and Applications (1998). 38 Dembo/Zeitouni, Large Deviations Techniques and Applications (1998). 39 Karatzas, Methods of Mathematical Finance (1998). 40 Fayolle/Iasnogorodski/ Malyshev, Random Walks in the Quarter-Plane (1999). 41 Aven/Jensen, Stochastic Models ...
Stochastic Modelling and Applied Probability
Stochastic Optimization. Stochastic Control. Stochastic Models in Life Sciences. Stochastic Modelling and Applied Probability. (Formerly: Applications of Mathematics). 38. Edited by B. Rozovski˘ı. G. Grimmett ... Amir Dembo r Ofer Zeitouni. Large Deviations Techniques and Applications. Corrected printing of the 1998 Edition ...
Applications of Mathematics
Mathematical Economics and Finance. Stochastic Optimization. Stochastic Control. Applications of. Mathematics. Stochastic Modelling and Applied Probability. 23. Edited by I. ... 3 Balakrishnan, Applied Functional Analysis, Second Edition (1981) ... 38 Dembo/Zeitouni, Large Deviations Techniques and Applications (1998).
Large Deviations of Heavy-Tailed Sums with Applications in Insurance
Large Deviations of Heavy-Tailed Sums with Applications in Insurance. Authors; Authors ... Large deviation techniques are then applied to randomly indexed sums and shot noise processes. We also indicate the ... large deviation heavy tails shot noise total claim amount Cramér–Lundberg model reinsurance ruin probability.
A conditional strong large deviation result and a functional central
Dec 4, 2014 ... and for the case Sn ∈ Rd (see [10]), but these have, to our knowledge, not been applied to ... For a general review of large deviation theory see for ex- ..... APPLICATIONS. 2.1. Stochastic model of T-cell activation. The immune system defends the body against dangerous intrusion, e.g. bacteria, viruses and ...
CELEBRATING 50 YEARS OF THE APPLIED PROBABILITY TRUST
large). The model considered is that of a Galton–Watson process. It is found that in some cases population paths exhibit the strange feature that population numbers go ... stochastic process. Large deviations theory asymptotically gives the probability that the path of the process is in a neighbourhood of a function u on [0,N].
Large deviations in mathematical finance
Jan 5, 2010 ... large deviations theory, and to illustrate how they are applied recently for example in stochastic volatility models to compute implied volatilities near maturities. Key words: large deviations, importance sampling, rare event simulation, exit probability, small time asymptotics, implied volatilities, credit risk, ...
RARE EVENT SIMULATION TECHNIQUES
applied to both light and heavy tailed systems and often are based on subsolutions to an associated Isaacs equation ... The successful application of large deviations theory in the design of efficient importance sampling ... sampling estimators in terms of a stochastic control problem in which the value function is the second.
Official Journal of the Bernoulli Society for Mathematical Statistics
Official Journal of the Bernoulli Society for Mathematical Statistics and Probability . Volume Twenty Two Number Four November 2016 ISSN: 1350-7265. The papers published in Bernoulli are indexed or abstracted in Current Index to Statistics,. Mathematical Reviews, Statistical Theory and Method Abstracts- Zentralblatt ...
A lower bound on the relative entropy with respect to a symmetric
Jan 7, 2015 ... Given two probability measures µ and ρ on R, the relative entropy of µ with respect to ρ (or the Kullback-Leibler divergence of ρ from µ) is ..... Large deviations techniques and applications, volume 38 of. Stochastic Modelling and Applied Probability. Springer-Verlag, 2010. MR-2571413. [4] Matthias Gorny.
Mean-field limit versus small-noise limit for some interacting particle
Sep 3, 2014 ... processes attracted by their own probability distribution: the so-called self- stabilizing processes. ... In the stochastic convergence framework, the large deviation theory plays an essential role for describing .... Using the law of large numbers applied to the sequence of independent and identically distributed ...
Some large deviations in Kingman's coalescent
Jan 20, 2015 ... in PROBABILITY. Some large deviations in Kingman's coalescent*. Andrej Depperschmidt†. Peter Pfaffelhuber‡. Annika Scheuringer†. Abstract. Kingman's coalescent is a random tree that arises from classical population genetic models such as the Moran model. Concerning the structure of the tree-top ...
Informational Confidence Bounds for Self-Normalized Averages and
Sep 13, 2013 ... to recommender systems and Big Data, and numerous variants have been considered (see [1] for a recent survey, and [2] for a related model). One possible solution ... mation Theory, have been successfully studied and used since then in many ..... cations, ser. Stochastic Modelling and Applied Probability.
Large deviations and gradient flows
Jan 22, 2012 ... flows with large deviations of stochastic processes. A particularly interesting ... ( quadratic) Wasserstein distance between two probability measures ρ0 and ρ1 with finite second moments is [18] ..... Wentzell theory for Brownian particles [10] shows how the mobility of a vector X = (X1,...,Xn) of n Brownian ...
A simple proof of a Kramers'type law for self-stabilizing diffusions in
Sep 30, 2017 ... (σ) as σ goes to 0 is the one of the large deviations for stochastic processes. Freidlin and Wentzell theory solves the exit- problem for time-homogeneous diffusions. Let us briefly introduce this theory. We refer the reader to [FW98, DZ98 ] for a complete review. We look at the diffusion xσ t = x0 + σβt − ∫.
Wiley Series in Probability and Statistics
DUPUIS and ELLIS • A Weak Convergence Approach to the Theory of Large Deviations. ETHIER and KURTZ ... LARSON • Introduction to Probability Theory and Statistical Inference, Third Edition. LESSLER and KALSBEEK ... BH AT • Elements of Applied Stochastic Processes, Second Edition. BHATTACHARYA and ...
Full Text (PDF)
Jun 23, 2015 ... cDipartimento di Fisica ed Astronomia, Università di Padova, I-35131 Padova, Italy; dInstitute of Information Theory and Automation, Academy of Sciences of the Czech ... Here, we apply large deviations theory and finite-sample ... retical models that pertain to the probability distribution of the random ...
Bibliography_Index
Sep 7, 2016 ... A general form of integral. Annals of Mathematics. Second Series,. 19(4):279– 294, 1918. [24] A. Dembo and O. Zeitouni. Large Deviations Techniques and Applications, volume 38 of Stochastic Modelling and Applied Probability. Springer-Verlag, Ber- lin, 2010. Corrected reprint of the second (1998) edition.
Anomalous Dependence on System Size of Large Deviation
therefore the large deviation functions are very important in the probability theory and the information theory. .... t¼0Ю the probability for paths with initial probability distribution Pрxр0ЮЮ. ..... [11] Dembo, A., and Zeitouni, O., Large Deviation Techniques and Applications, Volume 38 of Stochastic Modelling and Applied.