Project/Area Number  05452013 
Research Category 
GrantinAid for Scientific Research (B).

Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Nagoya University 
Principal Investigator 
IHARA Shunsuke Nagoya University, School of Informatics and Sciences, Professor, 情報文化学部, 教授 (00023200)

CoInvestigator(Kenkyūbuntansha) 
YOKOI Nideo Nagoya University, Graduate School of Human Informatics, Professor, 人間情報学研究科, 教授 (50023560)
ITO Masayuki Nagoya University, School of Informatics and Sciences, Professor, 情報文化学部, 教授 (60022638)
OZAWA Masanao Nagoya University School of Informatics and Sciences, Professor, 情報文化学部, 教授 (40126313)
長井 英生 名古屋大学, 情報文化学部, 助教授 (70110848)
SATO Keniti Nagoya University, School of Informatics and Sciences, Professor, 情報文化学部, 教授 (60015500)
村井 隆文 名古屋大学, 情報文化学部, 教授 (00109266)
MORIMOTO Hiroshi Nagoya University, School of Informatics and Sciences, Assoc.Professor, 情報文化学部, 助教授 (20115645)

Project Fiscal Year 
1993 – 1995

Project Status 
Completed(Fiscal Year 1995)

Budget Amount *help 
¥6,300,000 (Direct Cost : ¥6,300,000)
Fiscal Year 1995 : ¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1994 : ¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1993 : ¥2,300,000 (Direct Cost : ¥2,300,000)

Keywords  information theory / spectral analysis of stationary processes / maximum entropy method / large deviation theorem / channel capacity / 情報理論 / 定常過程のスペクトル解析 / 最大エントロピー法 / 大偏差定理 / 通信路容量 / ガウス型通信路 / 大偏差理論 
Research Abstract 
We have studied theory of stochastic processes and information theory, and obtained following results. (1) We investigate the large deviation theorems and their applications. First, we consider a signal detection problem in a continuous time white Gaussian channel. Suppose that one of two stationary signals is transmitted over the channel. Based on the observation of the output, we are required to decide which signal is sent. This is a kind of hypothesis testing problem. Using a large deviation theorem, we have shown that the error probability of the detection goes to zero exponentially fast. (2) It is known that the maximum entropy method is a method to estimate a spectral density function of a stationary proces. Using a large deviation theorem, we prove a limit theorem which shows that the maximum entropy method is optimal if the sample size is large enough. (3) Channel capacity, mutual information, and mean squre error play fundamental roles in information theory. We prove some inequalities for these quantities. These inequalities will play important roles in information theory. One of them is as follows. Let C be the feedback capacity of a communication channel with an additive noize Z,and denote by C^* the feedback capacity of the channel with Gaussian noize Z^* having the same covariance as Z.Then it is true that C^* < C < C^* + H (Z ; Z^*), where H (Z ; Z^*) denotes the relative entropy of Z with respect to Z^*.
