{"title":"ON THE EXISTENCE OF AN OPTIMAL STATIONARY I-POLICY IN NON-DISCOUNTED MARKOVIAN DECISION PROCESSES WITH INCOMPLETE STATE INFORMATION","authors":"M. Kurano","doi":"10.5109/13116","DOIUrl":"https://doi.org/10.5109/13116","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1977-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127399006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"THE SECOND PRINCIPLE OF OPTIMALITY","authors":"Seiichi Iwamoto","doi":"10.5109/13118","DOIUrl":"https://doi.org/10.5109/13118","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1977-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127353759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"DYADIC STATIONARY PROCESSES AND THEIR SPECTRAL REPRESENTATIONS","authors":"T. Nagai","doi":"10.5109/13115","DOIUrl":"https://doi.org/10.5109/13115","url":null,"abstract":"A class of random processes whose covariance functions are invariant under the shift by the dyadic addition is considered. These processes are called to be dyadic stationary. It is shown in theorem 2 that a dyadic stationary process has always spectral representation in terms of the system of Walsh functions parallel to an ordinary stationary process in terms of the system of trigonometric functions. By making use of spectral representation in terms of the system of Walsh functions, necessary and sufficient conditions for a dyadic stationary process to be a dyadic linear process introduced in Morettin (1974) are shown in theorems 3 and 4. 1. Preliminaries. We denote by I the set of all real numbers in the unit interval [0. 1] and by N the set of all non-negative integers. Let x and y be two non-negative real numbers and have the dyadic expansions : (1.1)x= E xk•2k, with xk=0 or 1 , (1.2)x= E yk•2k, with yk=0 or 1. k=-0. When the expansion, for instance say (1.1), is not unique, we adopt the expansion in which zeros appear infinitely often for xk, k<0. Then the dyadic addition e is defined by (1.3)x e Y= E (xk yk).2k , where xke yk denotes addition mod. 2 of {0, 1}, that is, 0 e 0=1 e 1=0 and le 0 =oe 1=1. (Cf. [4], [5].) AMS 1970 Subject classifications. Primary 60G10, 60B99; Secondary 10K35","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1977-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129687820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"STRUCTURE FORMATION OF SCIENTIFIC BRAINWARE AS A BASIS OF DATA BASE MANAGEMENT","authors":"T. Kitagawa","doi":"10.5109/13114","DOIUrl":"https://doi.org/10.5109/13114","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"310 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1977-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131431268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"THE EFFECT OF SWITCH-OVER DEVICE ON AVAILABILITY OF A 2-DISSIMILAR-UNIT REDUNDANT SYSTEM WITH A WARM STANDBY","authors":"M. Kodama, T. Itoi","doi":"10.5109/13112","DOIUrl":"https://doi.org/10.5109/13112","url":null,"abstract":"The effect of switch-over device on reliability of a 2-dissimilarunit redundant system with a warm standby is considered. The Laplace transform of the availability function and steady state availability are derived. The Laplace transform of the reliability function and the mean time to system failure are directly obtained from the Laplace transform of the availability function by suitable transformations. Therefore, a separate analysis of the reliability of the system is redundant. The steady state availability of the parallel and standby system with imperfect switchover are compared.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1977-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131335870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"BERRY-ESSEEN TYPE BOUND FOR DENSITY ESTIMATORS OF STATIONARY MARKOV PROCESSES","authors":"B. Rao","doi":"10.5109/13110","DOIUrl":"https://doi.org/10.5109/13110","url":null,"abstract":"Berry-Esseen type bound for the distribution function of a density estimator of kernel type is obtained when the observations are from a stationary Markov process. It is shown that the bound is of the order 0(n -1/3+τ ) for any τ>0 under some conditions.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1977-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115859563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A MATHEMATICAL FORMULATION OF INFORMATION NETWORK SYSTEM AND ITS IMPLICATIONS TO ARTIFICIAL INTELLIGENCE","authors":"T. Kitagawa","doi":"10.5109/13111","DOIUrl":"https://doi.org/10.5109/13111","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1977-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122319354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"ASYMPTOTIC DISTRIBUTION OF EIGENVALUES AND DEGENERATION OF SPARSE RANDOM MATRICES","authors":"S. Sato, Kingo Kobayashi","doi":"10.5109/13117","DOIUrl":"https://doi.org/10.5109/13117","url":null,"abstract":"This work is concerned with an asymptotical distribution of eigenvalues of sparse random matrices. It is shown that the semicircle law which is known for random matrices is also valid for the sparse random matrices with sparsity nIN=o(1), where n is the matrix size and 2N the number of non-zero elements of the matrix. The degree of degeneration is also estimated for the matrices with 2N—cn (c>0: const.) using knowledge of random graphs.","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1977-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122994824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"NONLINEAR PROGRAMMING IN BANACH SPACES WITH APPLICATIONS TO OPTIMAL CONTROL PROBLEMS","authors":"Shojiro Tagawa","doi":"10.5109/13103","DOIUrl":"https://doi.org/10.5109/13103","url":null,"abstract":"","PeriodicalId":287765,"journal":{"name":"Bulletin of Mathematical Statistics","volume":"169 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1976-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114733639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}