A V Skorohod

(Author)

Integration in Hilbert Space (Softcover Reprint of the Original 1st 1974)Paperback - Softcover Reprint of the Original 1st 1974, 12 November 2011

Integration in Hilbert Space (Softcover Reprint of the Original 1st 1974)
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Part of Series
Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge
Print Length
180 pages
Language
English
Publisher
Springer
Date Published
12 Nov 2011
ISBN-10
364265634X
ISBN-13
9783642656347

Description

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 statistics reduce 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. One must note that the language of probability theory tends to obscure the results obtained in these areas for mathematicians working in other fields. Another dir, ection leading to the study of integrals in function space is the theory and application of differential equations. A. N.

Product Details

Author:
A V Skorohod
Book Edition:
Softcover Reprint of the Original 1st 1974
Book Format:
Paperback
Country of Origin:
NL
Date Published:
12 November 2011
Dimensions:
22.86 x 15.24 x 1.07 cm
ISBN-10:
364265634X
ISBN-13:
9783642656347
Language:
English
Location:
Berlin, Heidelberg
Pages:
180
Publisher:
Weight:
272.16 gm

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