Minimum Action Curves in Degenerate Finsler Metrics - Existence and Properties (Paperback, 1st ed. 2015)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes in Mathematics, 2134
Release date:	July 2015
First published:	2015
Authors:	Matthias Heymann
Dimensions:	235 x 155 x 11mm (L x W x T)
Format:	Paperback
Pages:	186
Edition:	1st ed. 2015
ISBN-13:	978-3-319-17752-6
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics Books > Science & Mathematics > Mathematics > Geometry > General Books > Science & Mathematics > Mathematics > Optimization > General
LSN:	3-319-17752-4
Barcode:	9783319177526

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