Large deviation principle with generated pseudo measures

doi:10.1016/j.fss.2005.05.012

Fuzzy Sets and Systems

Volume 155, Issue 1, 1 October 2005, Pages 65-76

https://doi.org/10.1016/j.fss.2005.05.012 Get rights and content

Abstract

Contemporary large deviation theory uses various approaches. One of possible recent approaches is based on the idempotent $\sup$ -measure and related integrals based on operations $\sup$ and the usual product. In this paper, the large deviation convergence of a sequence of generated pseudo-measures to $\sup$ -decomposable measure is introduced. The main result of the paper gives a necessary condition for introduced convergence.

References (24)

R. Mesiar et al.
Idempotent integral as limit of $g$ -integrals
Fuzzy Sets and Systems
(1999)
L.A. Zadeh
Fuzzy sets as a basis for a theory of possibility
Fuzzy Sets and Systems
(1978)
A. de Acosta
Large deviations for empirical measures of Markov chains
J. Theoretical Probab.
(1990)
M. Akian, Densities of idempotent measures and large deviations, INRIA, Rapport de recherche, N 2534, Avril...
J.D. Deuschel et al.
Large Deviations
(1989)
A. Dembo, O. Zeitouni, Large Deviations Tehniques and Applications, second ed. Springer New York,...
M. D. Donsker, S. R. S. Varadhan, On some problems of large deviations for Markov process, Proc. 40th Session Int....
M.D. Donsker et al.
Large deviations for stationary Gaussian processes
Commun. Math. Phys.
(1985)
D. Dubois et al.
Possibility Theory
(1988)
P. Dupuis et al.
A Weak Convergence Approach to the Theory of Large Deviations
(1997)

R. S. Ellis, Entropy, large deviations, and statistical mechanics, Grundlehren der Mathematishen Wissenschaften...

R.S. Ellis

An overview of the theory of large deviations and applications to statistical mechanics

Scand. Actuarial J.

(1995)

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Large deviation principle with generated pseudo measures

Abstract

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Large deviations for empirical measures of Markov chains

J. Theoretical Probab.

Large Deviations

Large deviations for stationary Gaussian processes

Commun. Math. Phys.

Possibility Theory

A Weak Convergence Approach to the Theory of Large Deviations

An overview of the theory of large deviations and applications to statistical mechanics

Scand. Actuarial J.