{"title":"Comparison of Translation Experiments","authors":"E. Torgersen","doi":"10.1214/AOMS/1177692372","DOIUrl":"https://doi.org/10.1214/AOMS/1177692372","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"93 1","pages":"1383-1399"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82720525","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 Approximations for the Probability that a Sum of Lattice Random Vectors Lies in a Convex Set","authors":"J. K. Yarnold","doi":"10.1214/AOMS/1177692389","DOIUrl":"https://doi.org/10.1214/AOMS/1177692389","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"45 1","pages":"1566-1580"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79342946","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 Law of the Iterated Logarithm for the Range of Random Walk","authors":"N. Jain, W. Pruitt","doi":"10.1214/AOMS/1177692404","DOIUrl":"https://doi.org/10.1214/AOMS/1177692404","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"32 1","pages":"1692-1697"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75103642","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}
We give a mathematical definition of stationary, asymptotically memoryless, continuous-time channels, and prove a coding theorem and its converse for such channels.
给出了平稳、渐近无记忆连续信道的数学定义，并证明了该类信道的一个编码定理及其逆定理。
{"title":"Coding Theorem for Stationary, Asymptotically Memoryless, Continuous-time Channels","authors":"T. Kadota, A. Wyner","doi":"10.1214/AOMS/1177692392","DOIUrl":"https://doi.org/10.1214/AOMS/1177692392","url":null,"abstract":"We give a mathematical definition of stationary, asymptotically memoryless, continuous-time channels, and prove a coding theorem and its converse for such channels.","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"63 1","pages":"1603-1611"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75580088","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":"Error Estimates for the Weak Convergence to Certain Infinitely Divisible Laws","authors":"Thomas Hern","doi":"10.1214/AOMS/1177692391","DOIUrl":"https://doi.org/10.1214/AOMS/1177692391","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"38 1","pages":"1592-1602"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86171785","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":"On Estimation of Tail End Probabilities of the Sample Mean for Linear Stochastic Processes","authors":"K. Chanda","doi":"10.1214/AOMS/1177692402","DOIUrl":"https://doi.org/10.1214/AOMS/1177692402","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"10 2-3","pages":"1680-1686"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72460856","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}
It is the purpose of this paper to suggest, by a simple example, that the methods which have been so successful in the study of temporally homogeneous Markov processes can be applied equally successfully to general stochastic processes. Let i be a probability measure in the space Q, W) of all measures on the measurable space (Q, SW) of all functions wt) mapping R+ = (0, oo) into a measurable space (S, ?) where _ is the a-field generated by the events X,(wO) = w(t) C U C ? and where S is a separable compact space with Borel sets ?, and suppose that the continuous functions in Q have i-outer measure one. Let Tt, t C R+ be the semigroup of linear operators on (Q, ) defined by Tje(X1l C U1, *..., IXtn CUn) = [(Xt+tl C U1,***, Xt+tn C U.) and let Eu, U C ? be the resolution of the identity Eu M(A) = [(Xo C U, A). Let $ be the weak * closure over the continuous functions on the product topology of (Q, SW) of the linear subspace of (Q, S) which is generated by measures of the form Eun Ttn ... EU1 Tt1 i and let $+ be the set of all probability measures in O. Suppose now that T is the first exit time of X from the interior U of S and let g be a continuous function on the boundary U' of U. Let (* be the set of all linear functionals 0* on ( which are continuous in the weak * topology of O. Let Tt*o*o = O*Tto 0* C (* 0 D and G*0*0= limh oh-l[Th*0*0 00* e @ 0 e +
本文的目的是通过一个简单的例子表明，在研究时间齐次马尔可夫过程中如此成功的方法可以同样成功地应用于一般随机过程。设i是可测空间(Q, SW)上所有函数wt映射R+ = (0, oo)到可测空间(S， ?)的所有测度在空间Q, W)中的概率测度，其中_是事件X，(wO) = W (t) C U C ?其中S是一个具有Borel集合的可分离紧空间，并假设Q中的连续函数具有i-外测度1。设Tt, t C R+是(Q，)上的线性算子的半群，定义为Tje(x1 C U1， *…)， Xt+ tlc U1，***， Xt+ tlc U)，令Eu, uc ?设$为(Q, S)的线性子空间(Q, SW)的积拓扑上连续函数的弱*闭包，它是由形式为Eun Ttn…的测度生成的。EU1 Tt1我让美元+所有概率措施的集合T o .假设现在是第一个退出时间室内U (X)的S, g是一个连续函数的边界U '美国让(*较之线性泛函更具普遍意义的集合0 *(连续在弱*拓扑o .让Tt * * o = o C(* *参加0 * 0 D和g * 0 * 0 = limh oh-l (Th e * 0 * 0 00 * @ 0 e +
{"title":"Hitting Time Distributions for General Stochastic Processes","authors":"Dudley Paul Johnson","doi":"10.1214/AOMS/1177692408","DOIUrl":"https://doi.org/10.1214/AOMS/1177692408","url":null,"abstract":"It is the purpose of this paper to suggest, by a simple example, that the methods which have been so successful in the study of temporally homogeneous Markov processes can be applied equally successfully to general stochastic processes. Let i be a probability measure in the space Q, W) of all measures on the measurable space (Q, SW) of all functions wt) mapping R+ = (0, oo) into a measurable space (S, ?) where _ is the a-field generated by the events X,(wO) = w(t) C U C ? and where S is a separable compact space with Borel sets ?, and suppose that the continuous functions in Q have i-outer measure one. Let Tt, t C R+ be the semigroup of linear operators on (Q, ) defined by Tje(X1l C U1, *..., IXtn CUn) = [(Xt+tl C U1,***, Xt+tn C U.) and let Eu, U C ? be the resolution of the identity Eu M(A) = [(Xo C U, A). Let $ be the weak * closure over the continuous functions on the product topology of (Q, SW) of the linear subspace of (Q, S) which is generated by measures of the form Eun Ttn ... EU1 Tt1 i and let $+ be the set of all probability measures in O. Suppose now that T is the first exit time of X from the interior U of S and let g be a continuous function on the boundary U' of U. Let (* be the set of all linear functionals 0* on ( which are continuous in the weak * topology of O. Let Tt*o*o = O*Tto 0* C (* 0 D and G*0*0= limh oh-l[Th*0*0 00* e @ 0 e +","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"59 1","pages":"1716-1718"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80451582","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 Note on Fine and Tight Qualitative Probabilities","authors":"I. Niiniluoto","doi":"10.1214/AOMS/1177692390","DOIUrl":"https://doi.org/10.1214/AOMS/1177692390","url":null,"abstract":"","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"68 1","pages":"1581-1591"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80844595","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}
Sequential tests of separated hypotheses concerning the parameter θ of a Koopman-Darmois family are studied from the point of view of minimizing expected sample sizes pointwise in θ subject to error probability bounds. Sequential versions of the (generalized) likelihood ratio test are shown to exceed the minimum expected sample sizes by at most M log log α(-1) uniformly in θ, where α is the smallest error probability bound. The proof considers the likelihood ratio tests as ensembles of sequential probability ratio tests and compares them with alternative procedures by constructing alternative ensembles, applying a simple inequality of Wald and a new inequality of similar type. A heuristic approximation is given for the error probabilities of likelihood ratio tests, which provides an upper bound in the case of a normal mean.
{"title":"Likelihood ratio tests for sequential k-decision problems","authors":"G. Lorden","doi":"10.1214/AOMS/1177692374","DOIUrl":"https://doi.org/10.1214/AOMS/1177692374","url":null,"abstract":"Sequential tests of separated hypotheses concerning the parameter θ of a Koopman-Darmois family are studied from the point of view of minimizing expected sample sizes pointwise in θ subject to error probability bounds. Sequential versions of the (generalized) likelihood ratio test are shown to exceed the minimum expected sample sizes by at most M log log α(-1) uniformly in θ, where α is the smallest error probability bound. The proof considers the likelihood ratio tests as ensembles of sequential probability ratio tests and compares them with alternative procedures by constructing alternative ensembles, applying a simple inequality of Wald and a new inequality of similar type. A heuristic approximation is given for the error probabilities of likelihood ratio tests, which provides an upper bound in the case of a normal mean.","PeriodicalId":50764,"journal":{"name":"Annals of Mathematical Statistics","volume":"3 1","pages":"1412-1427"},"PeriodicalIF":0.0,"publicationDate":"1972-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88477271","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}
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