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Title: A General Conditional Large Deviation Principle

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:
 [1] ;  [2]
  1. Univ. of Texas, Austin, TX (United States). Applied Research Labs.
  2. Univ. of Texas, Austin, TX (United States). Dept. of Physics
Publication Date:
Grant/Contract Number:
FG03-94ER14465
Type:
Published Article
Journal Name:
Journal of Statistical Physics
Additional Journal Information:
Journal Volume: 161; Journal Issue: 1; Journal ID: ISSN 0022-4715
Publisher:
Springer
Research Org:
Texas Univ., Austin, TX (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); Univ. of Texas, Austin, TX (United States)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Large deviations; Conditional rate functions; Conditional distributions
OSTI Identifier:
1494369
Alternate Identifier(s):
OSTI ID: 1434928

La Cour, Brian R., and Schieve, William C.. A General Conditional Large Deviation Principle. United States: N. p., Web. doi:10.1007/s10955-015-1328-4.
La Cour, Brian R., & Schieve, William C.. A General Conditional Large Deviation Principle. United States. doi:10.1007/s10955-015-1328-4.
La Cour, Brian R., and Schieve, William C.. 2015. "A General Conditional Large Deviation Principle". United States. doi:10.1007/s10955-015-1328-4.
@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 = {2015},
month = {7}
}