{"title":"关于随机噪声的随机过程","authors":"T. Kawata","doi":"10.2996/KMJ/1138843604","DOIUrl":null,"url":null,"abstract":"If events are arrivals of electrons at the anode of vacuum tube, (l l) represents the noise current. The formulation (1.1) is due to J. L. Doob ί 1 ) Formally, the extensive analysis of random noise was done by S. O Rice, in the case \\ t Ct) is a trigonometric polynomial. The object of this paper is to prove some results, in connection with Rice theory, with X, (t) defined by (1.1) in a rather rigorous way from mathematical view points. The proofs of some known results are contained, because of completeness","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"On the stochastic process of random noise\",\"authors\":\"T. Kawata\",\"doi\":\"10.2996/KMJ/1138843604\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"If events are arrivals of electrons at the anode of vacuum tube, (l l) represents the noise current. The formulation (1.1) is due to J. L. Doob ί 1 ) Formally, the extensive analysis of random noise was done by S. O Rice, in the case \\\\ t Ct) is a trigonometric polynomial. The object of this paper is to prove some results, in connection with Rice theory, with X, (t) defined by (1.1) in a rather rigorous way from mathematical view points. The proofs of some known results are contained, because of completeness\",\"PeriodicalId\":318148,\"journal\":{\"name\":\"Kodai Mathematical Seminar Reports\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kodai Mathematical Seminar Reports\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2996/KMJ/1138843604\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kodai Mathematical Seminar Reports","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2996/KMJ/1138843604","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
摘要
如果事件是电子到达真空管的阳极，(l l)表示噪声电流。正式地说，随机噪声的广泛分析是由S. O . Rice完成的，在这种情况下，t (t)是一个三角多项式。本文的目的是用(1.1)所定义的X， (t)从数学的角度较为严格地证明与Rice理论有关的一些结果。由于完备性，一些已知结果的证明是包含的
If events are arrivals of electrons at the anode of vacuum tube, (l l) represents the noise current. The formulation (1.1) is due to J. L. Doob ί 1 ) Formally, the extensive analysis of random noise was done by S. O Rice, in the case \ t Ct) is a trigonometric polynomial. The object of this paper is to prove some results, in connection with Rice theory, with X, (t) defined by (1.1) in a rather rigorous way from mathematical view points. The proofs of some known results are contained, because of completeness
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