书目名称 | Integration in Hilbert Space |
编辑 | A. V. Skorohod |
视频video | http://file.papertrans.cn/469/468808/468808.mp4 |
丛书名称 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge |
图书封面 |  |
描述 | Integration in function spaces arose in probability theory when a gen eral theory of random processes was constructed. Here credit is cer tainly due to N. Wiener, who constructed a measure in function space, integrals-with respect to which express the mean value of functionals of Brownian motion trajectories. Brownian trajectories had previously been considered as merely physical (rather than mathematical) phe nomena. A. N. Kolmogorov generalized Wiener‘s construction to allow one to establish the existence of a measure corresponding to an arbitrary random process. These investigations were the beginning of the development of the theory of stochastic processes. A considerable part of this theory involves the solution of problems in the theory of measures on function spaces in the specific language of stochastic pro cesses. For example, finding the properties of sample functions is connected with the problem of the existence of a measure on some space; certain problems in statisticsreduce to the calculation of the density of one measure w. r. t. another one, and the study of transformations of random processes leads to the study of transformations of function spaces with measure |
出版日期 | Book 1974 |
关键词 | Calculation; Hilbert space; Hilbertscher Raum; Integralrechnung; Integration; Spaces; differential equatio |
版次 | 1 |
doi | https://doi.org/10.1007/978-3-642-65632-3 |
isbn_softcover | 978-3-642-65634-7 |
isbn_ebook | 978-3-642-65632-3 |
copyright | Springer-Verlag Berlin Heidelberg 1974 |