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001 978-3-319-17753-3
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020 _a9783319177533
_9978-3-319-17753-3
024 7 _a10.1007/978-3-319-17753-3
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aHeymann, Matthias.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMinimum Action Curves in Degenerate Finsler Metrics
_h[electronic resource] :
_bExistence and Properties /
_cby Matthias Heymann.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2015.
300 _aXV, 186 p. 14 illus., 11 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2134
520 _aPresenting 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.  .
650 0 _aDistribution (Probability theory.
650 0 _aGeometry.
650 0 _aMathematical optimization.
650 0 _aMathematics.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aGeometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21006
650 2 4 _aOptimization.
_0http://scigraph.springernature.com/things/product-market-codes/M26008
650 2 4 _aMathematics, general.
_0http://scigraph.springernature.com/things/product-market-codes/M00009
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319177540
776 0 8 _iPrinted edition:
_z9783319177526
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2134
856 4 0 _uhttps://doi.org/10.1007/978-3-319-17753-3
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10749
_d10749