A General Conditional Large Deviation Principle

La Cour, Brian R.; Schieve, William C.

doi:10.1007/s10955-015-1328-4

Title: A General Conditional Large Deviation Principle

Abstract

Given a sequence of Borel probability measures on a Hausdorff space which satisfy a large deviation principle (LDP), we consider the corresponding sequence of measures formed by conditioning on a set B. If the large deviation rate function I is good and effectively continuous, and the conditioning set has the property that (1) $$\overline{B°}$$=$$\overline{B}$$ and (2) I(x)<∞ for all xε$$\overline{B}$$, then the sequence of conditional measures satisfies a LDP with the good, effectively continuous rate function I_B, where I_B(x)=I(x)-inf I(B) if xε$$\overline{B}$$ and I_B(x)=∞ otherwise.

Authors:: La Cour, Brian R.; Schieve, William C.

Publication Date:: Sat Jul 18 00:00:00 EDT 2015

Research Org.:: Univ. of Texas, Austin, TX (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Univ. of Texas, Austin, TX (United States)

OSTI Identifier:: 1494369

Alternate Identifier(s):: OSTI ID: 1434928

Grant/Contract Number:: FG03-94ER14465

Resource Type:: Published Article

Journal Name:: Journal of Statistical Physics

Additional Journal Information:: Journal Name: Journal of Statistical Physics Journal Volume: 161 Journal Issue: 1; Journal ID: ISSN 0022-4715

Publisher:: Springer Science + Business Media

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Large deviations; Conditional rate functions; Conditional distributions

Citation Formats


                    La Cour, Brian R., and Schieve, William C. A General Conditional Large Deviation Principle.  United States: N. p., 2015. 
Web.  doi:10.1007/s10955-015-1328-4.

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                    La Cour, Brian R., & Schieve, William C. A General Conditional Large Deviation Principle.  United States.  https://doi.org/10.1007/s10955-015-1328-4

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                    La Cour, Brian R., and Schieve, William C. Sat .  
"A General Conditional Large Deviation Principle".  United States.  https://doi.org/10.1007/s10955-015-1328-4.

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@article{osti_1494369,

  title        = {A General Conditional Large Deviation Principle},

  author       = {La Cour, Brian R. and Schieve, William C.},

  abstractNote = {Given a sequence of Borel probability measures on a Hausdorff space which satisfy a large deviation principle (LDP), we consider the corresponding sequence of measures formed by conditioning on a set B. If the large deviation rate function I is good and effectively continuous, and the conditioning set has the property that (1) $\overline{B°}$=$\overline{B}$ and (2) I(x)<∞ for all xε$\overline{B}$, then the sequence of conditional measures satisfies a LDP with the good, effectively continuous rate function IB, where IB(x)=I(x)-inf I(B) if xε$\overline{B}$ and IB(x)=∞ otherwise.},

  doi          = {10.1007/s10955-015-1328-4},

  journal      = {Journal of Statistical Physics},

  number       = 1,

  volume       = 161,

  place        = {United States},

  year         = {Sat Jul 18 00:00:00 EDT 2015},

  month        = {Sat Jul 18 00:00:00 EDT 2015}

}

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Works referenced in this record:

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journal, January 2000

Ellis, Richard S.
Journal of Statistical Physics, Vol. 101, Issue 5/6, p. 999-1064
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Csiszar, Imre
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La Cour, Brian R.; Schieve, William C.
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journal, January 2000

La Cour, Brian R.; Schieve, William C.
Journal of Statistical Physics, Vol. 99, Issue 5/6, p. 1225-1249
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Title: A General Conditional Large Deviation Principle

Abstract

Citation Formats

Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles journal, January 2000

Entropy and equilibrium states in classical statistical mechanics book, January 1973

Microcanonical Distributions, Gibbs States, and the Equivalence of Ensembles book, January 1991

Sanov Property, Generalized $I$-Projection and a Conditional Limit Theorem journal, August 1984

Macroscopic Determinism in Interacting Systems Using Large Deviation Theory journal, January 2002

Maximum entropy and conditional probability journal, July 1981

Correlation Functionals journal, February 1965

The theory of large deviations: from Boltzmann’s 1877 calculation to equilibrium macrostates in 2D turbulence journal, September 1999

Macroscopic Determinism in Noninteracting Systems Using Large Deviation Theory journal, January 2000

Large Deviation Principles and Complete Equivalence and Nonequivalence Results for Pure and Mixed Ensembles
journal, January 2000

Entropy and equilibrium states in classical statistical mechanics
book, January 1973

Microcanonical Distributions, Gibbs States, and the Equivalence of Ensembles
book, January 1991

Sanov Property, Generalized $I$-Projection and a Conditional Limit Theorem
journal, August 1984

Macroscopic Determinism in Interacting Systems Using Large Deviation Theory
journal, January 2002

Maximum entropy and conditional probability
journal, July 1981

Correlation Functionals
journal, February 1965

The theory of large deviations: from Boltzmann’s 1877 calculation to equilibrium macrostates in 2D turbulence
journal, September 1999

Macroscopic Determinism in Noninteracting Systems Using Large Deviation Theory
journal, January 2000