书目名称 | White Noise | 副标题 | An Infinite Dimensio | 编辑 | Takeyuki Hida,Hui-Hsiung Kuo,Ludwig Streit | 视频video | | 丛书名称 | Mathematics and Its Applications | 图书封面 |  | 描述 | Many areas of applied mathematics call for an efficient calculus in infinite dimensions. This is most apparent in quantum physics and in all disciplines of science which describe natural phenomena by equations involving stochasticity. With this monograph we intend to provide a framework for analysis in infinite dimensions which is flexible enough to be applicable in many areas, and which on the other hand is intuitive and efficient. Whether or not we achieved our aim must be left to the judgment of the reader. This book treats the theory and applications of analysis and functional analysis in infinite dimensions based on white noise. By white noise we mean the generalized Gaussian process which is (informally) given by the time derivative of the Wiener process, i.e., by the velocity of Brownian mdtion. Therefore, in essence we present analysis on a Gaussian space, and applications to various areas of sClence. Calculus, analysis, and functional analysis in infinite dimensions (or dimension-free formulations of these parts of classical mathematics) have a long history. Early examples can be found in the works of Dirichlet, Euler, Hamilton, Lagrange, and Riemann on variational problem | 出版日期 | Book 1993 | 关键词 | Brownian motion; Dirichlet form; Markov process; Potential; Probability theory; measure theory | 版次 | 1 | doi | https://doi.org/10.1007/978-94-017-3680-0 | isbn_softcover | 978-90-481-4260-6 | isbn_ebook | 978-94-017-3680-0 | copyright | Springer Science+Business Media B.V. 1993 |
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