In this paper we show some new look at large deviation theorems from the viewpoint of the information-spectrum (IS) methods, which has been first exploited in information theory, and also demonstrate a new basic formula for the large deviation rate function in general, which is expressed as a pair of the lower and upper IS rate functions. In particular, we are interested in establishing the general large deviation rate functions that are derivable as the Fenchel-Legendre transform of the cumulant generating function. The final goal is to show, under some mild condition, a necessary and sufficient condition for the IS rate function to be derivable as the Fenchel-Legendre transform of the cumulant generating function, i.e., to be a rate function of Gartner-Ellis type.
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Te-Sun HAN, "Large Deviation Theorems Revisited: Information-Spectrum Approach" in IEICE TRANSACTIONS on Fundamentals,
vol. E91-A, no. 10, pp. 2704-2719, October 2008, doi: 10.1093/ietfec/e91-a.10.2704.
Abstract: In this paper we show some new look at large deviation theorems from the viewpoint of the information-spectrum (IS) methods, which has been first exploited in information theory, and also demonstrate a new basic formula for the large deviation rate function in general, which is expressed as a pair of the lower and upper IS rate functions. In particular, we are interested in establishing the general large deviation rate functions that are derivable as the Fenchel-Legendre transform of the cumulant generating function. The final goal is to show, under some mild condition, a necessary and sufficient condition for the IS rate function to be derivable as the Fenchel-Legendre transform of the cumulant generating function, i.e., to be a rate function of Gartner-Ellis type.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e91-a.10.2704/_p
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@ARTICLE{e91-a_10_2704,
author={Te-Sun HAN, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Large Deviation Theorems Revisited: Information-Spectrum Approach},
year={2008},
volume={E91-A},
number={10},
pages={2704-2719},
abstract={In this paper we show some new look at large deviation theorems from the viewpoint of the information-spectrum (IS) methods, which has been first exploited in information theory, and also demonstrate a new basic formula for the large deviation rate function in general, which is expressed as a pair of the lower and upper IS rate functions. In particular, we are interested in establishing the general large deviation rate functions that are derivable as the Fenchel-Legendre transform of the cumulant generating function. The final goal is to show, under some mild condition, a necessary and sufficient condition for the IS rate function to be derivable as the Fenchel-Legendre transform of the cumulant generating function, i.e., to be a rate function of Gartner-Ellis type.},
keywords={},
doi={10.1093/ietfec/e91-a.10.2704},
ISSN={1745-1337},
month={October},}
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TY - JOUR
TI - Large Deviation Theorems Revisited: Information-Spectrum Approach
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2704
EP - 2719
AU - Te-Sun HAN
PY - 2008
DO - 10.1093/ietfec/e91-a.10.2704
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E91-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2008
AB - In this paper we show some new look at large deviation theorems from the viewpoint of the information-spectrum (IS) methods, which has been first exploited in information theory, and also demonstrate a new basic formula for the large deviation rate function in general, which is expressed as a pair of the lower and upper IS rate functions. In particular, we are interested in establishing the general large deviation rate functions that are derivable as the Fenchel-Legendre transform of the cumulant generating function. The final goal is to show, under some mild condition, a necessary and sufficient condition for the IS rate function to be derivable as the Fenchel-Legendre transform of the cumulant generating function, i.e., to be a rate function of Gartner-Ellis type.
ER -