| 书目名称 | Random Fields and Stochastic Partial Differential Equations | | 编辑 | Yu. A. Rozanov | | 视频video | | | 丛书名称 | Mathematics and Its Applications | | 图书封面 |  | | 描述 | This book considers some models described by means of partial dif ferential equations and boundary conditions with chaotic stochastic disturbance. In a framework of stochastic Partial Differential Equa tions an approach is suggested to generalize solutions of stochastic Boundary Problems. The main topic concerns probabilistic aspects with applications to well-known Random Fields models which are representative for the corresponding stochastic Sobolev spaces. {The term "stochastic" in general indicates involvement of appropriate random elements. ) It assumes certain knowledge in general Analysis and Probability {Hilbert space methods, Schwartz distributions, Fourier transform) . I A very general description of the main problems considered can be given as follows. Suppose, we are considering a random field ~ in a region T ~ Rd which is associated with a chaotic (stochastic) source"‘ by means of the differential equation (*) in T. A typical chaotic source can be represented by an appropri ate random field"‘ with independent values, i. e. , generalized random function"‘ = ( cp, ‘TJ), cp E C~(T), with independent random variables ( cp, ‘fJ) for any test functions cp with disjoint sup | | 出版日期 | Book 1998 | | 关键词 | Probability theory; Sobolev space; partial differential equation; random function; stochastic processes; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-017-2838-6 | | isbn_softcover | 978-90-481-5009-0 | | isbn_ebook | 978-94-017-2838-6 | | copyright | Springer Science+Business Media B.V. 1998 |
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发表于 2025-3-21 19:13:52
