國立高雄大學圖資館 |

Local limit theorems for inhomogeneous Markov chains

Record Type:	Electronic resources : Monograph/item
Title/Author:	Local limit theorems for inhomogeneous Markov chainsby Dmitry Dolgopyat, Omri M. Sarig.
Author:	Dolgopyat, Dmitry.
other author:	Sarig, Omri M.
Published:	Cham :Springer International Publishing :2023.
Description:	xiii, 342 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Limit theorems (Probability theory)
Online resource:	https://doi.org/10.1007/978-3-031-32601-1
ISBN:	9783031326011$q(electronic bk.)

Local limit theorems for inhomogeneous Markov chains
Dolgopyat, Dmitry.

Local limit theorems for inhomogeneous Markov chains[electronic resource] /by Dmitry Dolgopyat, Omri M. Sarig. - Cham :Springer International Publishing :2023. - xiii, 342 p. :ill., digital ;24 cm. - Lecture notes in mathematics,v. 23311617-9692 ;. - Lecture notes in mathematics ;2035..

This book extends the local central limit theorem to inhomogeneous Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. It develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of numerous examples, a comprehensive review of the literature, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, random walks in random environments, random dynamical systems and non-stationary systems.

ISBN: 9783031326011$q(electronic bk.)

Standard No.: 10.1007/978-3-031-32601-1doiSubjects--Topical Terms:

182695
Limit theorems (Probability theory)

LC Class. No.: QA273.67

Dewey Class. No.: 519.2

Local limit theorems for inhomogeneous Markov chains
LDR:02257nmm a2200349 a 4500 001 648835
003 DE-He213
005 20230731231845.0
006 m d
007 cr nn 008maaau
008 240116s2023 sz s 0 eng d
020 $a 9783031326011$q(electronic bk.)
020 $a 9783031326004$q(paper)
024 7 $a 10.1007/978-3-031-32601-1 $2 doi
035 $a 978-3-031-32601-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA273.67
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
090 $a QA273.67 $b .D664 2023
100 1 $a Dolgopyat, Dmitry. $3 958692
245 1 0 $a Local limit theorems for inhomogeneous Markov chains $h [electronic resource] / $c by Dmitry Dolgopyat, Omri M. Sarig.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2023.
300 $a xiii, 342 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in mathematics, $x 1617-9692 ; $v v. 2331
520 $a This book extends the local central limit theorem to inhomogeneous Markov chains whose state spaces and transition probabilities are allowed to change in time. Such chains are used to model Markovian systems depending on external time-dependent parameters. It develops a new general theory of local limit theorems for additive functionals of Markov chains, in the regimes of local, moderate, and large deviations, and provides nearly optimal conditions for the classical expansions, as well as asymptotic corrections when these conditions fail. Applications include local limit theorems for independent but not identically distributed random variables, Markov chains in random environments, and time-dependent perturbations of homogeneous Markov chains. The inclusion of numerous examples, a comprehensive review of the literature, and an account of the historical background of the subject make this self-contained book accessible to graduate students. It will also be useful for researchers in probability and ergodic theory who are interested in asymptotic behaviors, random walks in random environments, random dynamical systems and non-stationary systems.
650 0 $a Limit theorems (Probability theory) $3 182695
650 0 $a Markov processes. $3 181910
650 1 4 $a Probability Theory. $3 913371
650 2 4 $a Stochastic Processes. $3 743764
650 2 4 $a Dynamical Systems. $3 913342
700 1 $a Sarig, Omri M. $3 958693
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Lecture notes in mathematics ; $v 2035. $3 557764
856 4 0 $u https://doi.org/10.1007/978-3-031-32601-1
950 $a Mathematics and Statistics (SpringerNature-11649)