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]}
 Univ. of Texas, Austin, TX (United States). Applied Research Labs.
 Univ. of Texas, Austin, TX (United States). Dept. of Physics
 Publication Date:
 Grant/Contract Number:
 FG0394ER14465
 Type:
 Published Article
 Journal Name:
 Journal of Statistical Physics
 Additional Journal Information:
 Journal Volume: 161; Journal Issue: 1; Journal ID: ISSN 00224715
 Publisher:
 Springer
 Research Org:
 Texas Univ., Austin, TX (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22); 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/s1095501513284.
La Cour, Brian R., & Schieve, William C.. A General Conditional Large Deviation Principle. United States. doi:10.1007/s1095501513284.
La Cour, Brian R., and Schieve, William C.. 2015.
"A General Conditional Large Deviation Principle". United States.
doi:10.1007/s1095501513284.
@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/s1095501513284},
journal = {Journal of Statistical Physics},
number = 1,
volume = 161,
place = {United States},
year = {2015},
month = {7}
}