國立虎尾科技大學 |

Language: English

Back

Continuous Paths in Brownian Motion ...

University of California, Berkeley.

Continuous Paths in Brownian Motion and Related Problems.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Continuous Paths in Brownian Motion and Related Problems./
Author:	Tang, Wenpin.
Description:	1 online resource (84 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Contained By:	Dissertation Abstracts International78-12B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355263091

Continuous Paths in Brownian Motion and Related Problems.
Tang, Wenpin.

Continuous Paths in Brownian Motion and Related Problems. - 1 online resource (84 pages)

Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

This thesis is composed of six chapters, which mainly deals with embedding continuous paths in Brownian motion. It is adapted from two publications [123, 124], joint with Jim Pitman.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355263091Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Continuous Paths in Brownian Motion and Related Problems.
LDR:02835ntm a2200421Ki 4500 001 909760
005 20180426091045.5
006 m o u
007 cr mn||||a|a||
008 190606s2017 xx obm 000 0 eng d
020 $a 9780355263091
035 $a (MiAaPQ)AAI10270135
035 $a (MiAaPQ)berkeley:16808
035 $a AAI10270135
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Tang, Wenpin. $3 1180697
245 1 0 $a Continuous Paths in Brownian Motion and Related Problems.
264 0 $c 2017
300 $a 1 online resource (84 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-12(E), Section: B.
500 $a Adviser: James Pitman.
502 $a Thesis (Ph.D.) $c University of California, Berkeley $d 2017.
504 $a Includes bibliographical references
520 $a This thesis is composed of six chapters, which mainly deals with embedding continuous paths in Brownian motion. It is adapted from two publications [123, 124], joint with Jim Pitman.
520 $a We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptotics of the expected waiting time for several interesting patterns. These suggest corresponding results on the existence/non-existence of continuous paths embedded in Brownian motion.
520 $a By various stochastic analysis arguments (path decomposition, Ito excursion theory, potential theory...), we are able to prove some of these existence and non-existence results:
520 $a [special characters omitted].
520 $a where e is a normalized Brownian excursion, V(b) is the Vervaat transform of Brownian bridge ending at lambda, m is a Brownian meander, and R is the three dimensional Bessel process of unit length.
520 $a The question of embedding a Brownian bridge into Brownian motion is more chanllenging. After explaining why some simple or traditional approaches do not work, we make use of recent work of Last and Thorisson on shift couplings of stationary random measures to prove the result. These can be applied after a thorough analysis of the Slepian zero set {t ≥ 0; Bt = Bt+1}.
520 $a We also discuss the potential theoretical aspect of embedding continuous paths in a random process. A list of open problems is presented.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Statistics. $3 556824
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0463
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of California, Berkeley. $b Statistics. $3 1180698
773 0 $t Dissertation Abstracts International $g 78-12B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10270135 $z click for full text (PQDT)

based on 0 review(s)

Multimedia

Reviews

Add a review and share your thoughts with other readers

Export

pickup library