About this book
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.
- Book Title Minimum Action Curves in Degenerate Finsler Metrics
- Book Subtitle Existence and Properties
- Series Title Lecture Notes in Mathematics
- Series Abbreviated Title Lect.Notes Mathematics
- DOI https://doi.org/10.1007/978-3-319-17753-3
- Copyright Information Springer International Publishing Switzerland 2015
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Softcover ISBN 978-3-319-17752-6
- eBook ISBN 978-3-319-17753-3
- Series ISSN 0075-8434
- Series E-ISSN 1617-9692
- Edition Number 1
- Number of Pages XV, 186
- Number of Illustrations 3 b/w illustrations, 11 illustrations in colour
Probability Theory and Stochastic Processes
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