| 书目名称 | Probability in Banach Spaces, 8: Proceedings of the Eighth International Conference | | 编辑 | Richard M. Dudley,Marjorie G. Hahn,James Kuelbs | | 视频video | | | 丛书名称 | Progress in Probability | | 图书封面 |  | | 描述 | Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970‘s. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950‘s and developed strongly in the 1960‘s and 70‘s. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70‘s a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in s | | 出版日期 | Conference proceedings 1992 | | 关键词 | Brownian motion; Gaussian measure; Gaussian process; Markov process; Martingale; Random variable; distribu | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4612-0367-4 | | isbn_softcover | 978-1-4612-6728-7 | | isbn_ebook | 978-1-4612-0367-4Series ISSN 1050-6977 Series E-ISSN 2297-0428 | | issn_series | 1050-6977 | | copyright | Springer Science+Business Media New York 1992 |
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