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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.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E91-A No.10 pp.2704-2719

- Publication Date
- 2008/10/01

- Publicized

- Online ISSN
- 1745-1337

- DOI
- 10.1093/ietfec/e91-a.10.2704

- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)

- Category
- Information Theory

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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 -