大葉大學圖書館 |

Minimum action curves in degenerate Finsler metrics[electronic resource] :existence and properties /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	516.375
書名/作者:	Minimum action curves in degenerate Finsler metrics : existence and properties // by Matthias Heymann.
作者:	Heymann, Matthias.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xv, 186 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Finsler spaces.
標題:	Mathematics.
標題:	Probability Theory and Stochastic Processes.
標題:	Geometry.
標題:	Optimization.
標題:	Mathematics, general.
ISBN:	9783319177533 (electronic bk.)
ISBN:	9783319177526 (paper)
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-17753-3

Minimum action curves in degenerate Finsler metrics[electronic resource] :existence and properties /
Heymann, Matthias.

Minimum action curves in degenerate Finsler metricsexistence and properties /[electronic resource] :by Matthias Heymann. - Cham :Springer International Publishing :2015. - xv, 186 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21340075-8434 ;. - Lecture notes in mathematics ;2035..

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.

ISBN: 9783319177533 (electronic bk.)

Standard No.: 10.1007/978-3-319-17753-3doiSubjects--Topical Terms:

444408
Finsler spaces.

LC Class. No.: QA689 / .H49 2015

Dewey Class. No.: 516.375

Minimum action curves in degenerate Finsler metrics[electronic resource] :existence and properties /
LDR:02099nam a2200325 a 4500 001 443184
003 DE-He213
005 20160217165541.0
006 m d
007 cr nn 008maaau
008 160715s2015 gw s 0 eng d
020 $a 9783319177533 (electronic bk.)
020 $a 9783319177526 (paper)
024 7 $a 10.1007/978-3-319-17753-3 $2 doi
035 $a 978-3-319-17753-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA689 $b .H49 2015
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
082 0 4 $a 516.375 $2 23
090 $a QA689 $b .H618 2015
100 1 $a Heymann, Matthias. $3 633612
245 1 0 $a Minimum action curves in degenerate Finsler metrics $h [electronic resource] : $b existence and properties / $c by Matthias Heymann.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xv, 186 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2134
520 $a 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.
650 0 $a Finsler spaces. $3 444408
650 0 $a Mathematics. $3 172349
650 2 4 $a Probability Theory and Stochastic Processes. $3 463894
650 2 4 $a Geometry. $3 382374
650 2 4 $a Optimization. $3 463683
650 2 4 $a Mathematics, general. $3 464903
710 2 $a SpringerLink (Online service) $3 463450
773 0 $t Springer eBooks
830 0 $a Lecture notes in mathematics ; $v 2035. $3 464096
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-17753-3
950 $a Mathematics and Statistics (Springer-11649)