| 书目名称 | Minimum Action Curves in Degenerate Finsler Metrics |
| 副标题 | Existence and Proper |
| 编辑 | Matthias Heymann |
| 视频video | |
| 概述 | Explores the non-standard geometric view of the Wentzell-Freidlin theory of rare transition events.The general geometric framework may spawn applications outside of probability theory.Key results and |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | .Presenting a study of geometric action functionals (i.e., non-negative functionals on the space of unparameterized oriented rectifiable curves), this monograph focuses on the subclass of those functionals whose local action is a degenerate type of Finsler metric that may vanish in certain directions, allowing for curves with positive Euclidean length but with zero action. For such functionals, criteria are developed under which there exists a minimum action curve leading from one given set to another. Then the properties of this curve are studied, and the non-existence of minimizers is established in some settings..Applied to a geometric reformulation of the quasipotential of Wentzell-Freidlin theory (a subfield of large deviation theory), these results can yield the existence and properties of maximum likelihood transition curves between two metastable states in a stochastic process with small noise..The book assumes only standard knowledge in graduate-level analysis; all higher-level mathematical concepts are introduced along the way.. . |
| 出版日期 | Book 2015 |
| 关键词 | 60F10, 51-02, 49J45; Action functional; Large deviation theory; Minimizer; Quasipotential; Wentzell-Freid |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-319-17753-3 |
| isbn_softcover | 978-3-319-17752-6 |
| isbn_ebook | 978-3-319-17753-3Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | Springer International Publishing Switzerland 2015 |
发表于 2025-3-21 17:33:23
