書目名稱 | Gaussian Random Processes |
編輯 | I. A. Ibragimov,Y. A. Rozanov |
視頻video | http://file.papertrans.cn/381/380957/380957.mp4 |
叢書名稱 | Stochastic Modelling and Applied Probability |
圖書封面 |  |
描述 | The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva- lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par- ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam- ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys- tematic presentation of the basic results can be found, for instance, |
出版日期 | Book 1978 |
關(guān)鍵詞 | Ergodic theory; Gaussian measure; Gaussscher Prozess; Station?rer Prozess; mixing; probability measure; ra |
版次 | 1 |
doi | https://doi.org/10.1007/978-1-4612-6275-6 |
isbn_softcover | 978-1-4612-6277-0 |
isbn_ebook | 978-1-4612-6275-6Series ISSN 0172-4568 Series E-ISSN 2197-439X |
issn_series | 0172-4568 |
copyright | Springer-Verlag New York Inc. 1978 |