| 書目名稱 | Levy Processes, Integral Equations, Statistical Physics: Connections and Interactions | | 編輯 | Lev A. Sakhnovich | | 視頻video | http://file.papertrans.cn/586/585423/585423.mp4 | | 概述 | Investigation of the interconnection between probability problems and analysis problems.Consideration of the statistical problems using the game theory ideas.Construction of special examples instead o | | 叢書名稱 | Operator Theory: Advances and Applications | | 圖書封面 |  | | 描述 | In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis also plays a central role in the present book. However, our approach is mainly based on the application of analysis methods (the method of operator identities, integral equations theory, dual systems, integrable equations) to probability theory (Levy processes, M. Kac‘s problems, the principle of imperceptibility of the boundary, signal theory). The essential part of the book is dedicated to problems of statistical physics (classical and quantum cases). We consider the corresponding statistical problems (Gibbs-type formulas, non-extensive statistical mechanics, Boltzmann equation) from the game point of view (the game between energy and entropy). One chapter is dedicated to the construction of special examples instead of existence theorems (D. Larson‘s theorem, Ringrose‘s hypothesis, the Kadison-Singer and Gohberg-Krein questions). We also investigate the Bezoutiant operator. In this context, we do not make the assumption that the Bezoutiant operator is normally solvable, allowing us t | | 出版日期 | Book 2012 | | 關(guān)鍵詞 | Levy processes; energy; entropy; stable processes; triangular factorization; combinatorics | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-0348-0356-4 | | isbn_softcover | 978-3-0348-0801-9 | | isbn_ebook | 978-3-0348-0356-4Series ISSN 0255-0156 Series E-ISSN 2296-4878 | | issn_series | 0255-0156 | | copyright | Springer Basel 2012 |
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