東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Some Topics in Large Deviations Theo...

Chen, Jiang.

Linked to FindBook

Google Book

Amazon

博客來

Some Topics in Large Deviations Theory for Stochastic Dynamical Systems.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Some Topics in Large Deviations Theory for Stochastic Dynamical Systems./
Author:	Chen, Jiang.
Description:	206 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.
Contained By:	Dissertation Abstracts International74-09B(E).
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3562874
ISBN:	9781303107405

Some Topics in Large Deviations Theory for Stochastic Dynamical Systems.
Chen, Jiang.

Some Topics in Large Deviations Theory for Stochastic Dynamical Systems. - 206 p.

Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.

Thesis (Ph.D.)--The University of North Carolina at Chapel Hill, 2013.

In this dissertation, we study large deviations problems for stochastic dynamical systems. First, we consider a family of Stochastic Partial Differential Equations (SPDE) driven by a Poisson Random Measure (PRM) that are motivated by problems of chemical/pollutant dispersal. We established a Large Deviation Principle (LDP) for the long time profile of the chemical concentration using techniques based on variational representations for nonnegative functionals of general PRM. Second, we develop a LDP for small Poisson noise perturbations of a general class of deterministic infinite dimensional models. SPDEs driven by PRM have been proposed as models for many different physical systems. The approach taken here, which is based on variational representations, reduces the proof of the LDP to establishing basic qualitative properties for controlled analogues of the underlying stochastic system. Third, we study stochastic systems with two time scales. Such multiscale systems arise in many applications in engineering, operations research and biological and physical sciences. The models considered in this dissertation are usually referred to as systems with "full dependence'', which refers to the feature that the coefficients of both the slow and the fast processes depend on both variables. We establish a LDP for such systems with degenerate diffusion coefficients.

ISBN: 9781303107405Subjects--Topical Terms:

515831
Mathematics.

Some Topics in Large Deviations Theory for Stochastic Dynamical Systems.
LDR:03248nam a2200301 4500 001 1959349
005 20140520124008.5
008 150210s2013 ||||||||||||||||| ||eng d
020 $a 9781303107405
035 $a (MiAaPQ)AAI3562874
035 $a AAI3562874
040 $a MiAaPQ $c MiAaPQ
100 1 $a Chen, Jiang. $3 1917886
245 1 0 $a Some Topics in Large Deviations Theory for Stochastic Dynamical Systems.
300 $a 206 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-09(E), Section: B.
500 $a Adviser: Amarjit Budhiraja.
502 $a Thesis (Ph.D.)--The University of North Carolina at Chapel Hill, 2013.
520 $a In this dissertation, we study large deviations problems for stochastic dynamical systems. First, we consider a family of Stochastic Partial Differential Equations (SPDE) driven by a Poisson Random Measure (PRM) that are motivated by problems of chemical/pollutant dispersal. We established a Large Deviation Principle (LDP) for the long time profile of the chemical concentration using techniques based on variational representations for nonnegative functionals of general PRM. Second, we develop a LDP for small Poisson noise perturbations of a general class of deterministic infinite dimensional models. SPDEs driven by PRM have been proposed as models for many different physical systems. The approach taken here, which is based on variational representations, reduces the proof of the LDP to establishing basic qualitative properties for controlled analogues of the underlying stochastic system. Third, we study stochastic systems with two time scales. Such multiscale systems arise in many applications in engineering, operations research and biological and physical sciences. The models considered in this dissertation are usually referred to as systems with "full dependence'', which refers to the feature that the coefficients of both the slow and the fast processes depend on both variables. We establish a LDP for such systems with degenerate diffusion coefficients.
520 $a The last part of this dissertation focuses on numerical schemes for computing invariant measures of reflected diffusions. Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the corresponding stochastic networks and thus it is important to develop reliable and efficient algorithms for numerical computation of such distributions. We propose and analyze a Monte-Carlo scheme based on an Euler type discretization. We prove an almost sure consistency of the appropriately weighted empirical measures constructed from the simulated discretized reflected diffusion to the true diffusion model. Rates of convergence are also obtained for certain class of test functions. Some numerical examples are presented to illustrate the applicability of this approach.
590 $a School code: 0153.
650 4 $a Mathematics. $3 515831
650 4 $a Statistics. $3 517247
650 4 $a Applied Mathematics. $3 1669109
690 $a 0405
690 $a 0463
690 $a 0364
710 2 $a The University of North Carolina at Chapel Hill. $b Statistics. $3 2094745
773 0 $t Dissertation Abstracts International $g 74-09B(E).
790 $a 0153
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3562874