Large Deviation Theorems Revisited: Information-Spectrum Approach

• HAN Te-Sun

  Faculty of Science and Engineering, Waseda University The Institute of Electronics, Information and Communication Engineers

抄録

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 Gärtner-Ellis type.

収録刊行物

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E91-A (10), 2704-2719, 2008

  一般社団法人 電子情報通信学会

キーワード

• large deviation
• information-spectrum
• rate functions
• cumulant generating function
• Gärtner-Ellis theorem
• Fenchel-Legengre transformation
• general source

詳細情報

• CRID: 1390001206310403328
• NII論文ID: 10026852249
• NII書誌ID: AA10826239
• DOI: 10.1093/ietfec/e91-a.10.2704
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E91.A/10/E91.A_10_2704/_pdf
• 本文言語コード: en
• データソース種別:
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• 抄録ライセンスフラグ: 使用不可