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Numerical Solution of Stochastic Control Problems Using the Finite Element Method.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Numerical Solution of Stochastic Control Problems Using the Finite Element Method./
Author:	Vieten, Martin G.
Description:	1 online resource (239 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-09(E), Section: B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355990805

Numerical Solution of Stochastic Control Problems Using the Finite Element Method.
Vieten, Martin G.

Numerical Solution of Stochastic Control Problems Using the Finite Element Method. - 1 online resource (239 pages)

Source: Dissertation Abstracts International, Volume: 79-09(E), Section: B.

Thesis (Ph.D.)--The University of Wisconsin - Milwaukee, 2018.

Includes bibliographical references

Based on linear programming formulations for infinite horizon stochastic control problems, a numerical technique in fashion of the finite element method is developed. The convergence of the approximate scheme is shown and its performance is illustrated on multiple examples. This thesis begins with an introduction of stochastic optimal control and a review of the theory of the linear programming approach. The analysis of existence and uniqueness of solutions to the linear programming formulation for fixed controls represents the first contribution of this work. Then, an approximate scheme for the linear programming formulations is established. To this end, a novel discretization of the involved measures and constraints using finite dimensional function subspaces is introduced. Its convergence is proven using weak convergence of measures, and a detailed analysis of the approximate relaxed controls. The applicability of the established method is shown through a collection of examples from stochastic control. The considered examples include models with bounded or unbounded state space, models featuring continuous and singular control as well as discounted or long-term average cost criteria. Analyses of various model parameters are given, and in selected examples, the approximate solutions are compared to available analytic solutions. A summary and an outlook on possible research directions is given.

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

Mode of access: World Wide Web

ISBN: 9780355990805Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Numerical Solution of Stochastic Control Problems Using the Finite Element Method.
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500 $a Source: Dissertation Abstracts International, Volume: 79-09(E), Section: B.
500 $a Adviser: Richard H. Stockbridge.
502 $a Thesis (Ph.D.)--The University of Wisconsin - Milwaukee, 2018.
504 $a Includes bibliographical references
520 $a Based on linear programming formulations for infinite horizon stochastic control problems, a numerical technique in fashion of the finite element method is developed. The convergence of the approximate scheme is shown and its performance is illustrated on multiple examples. This thesis begins with an introduction of stochastic optimal control and a review of the theory of the linear programming approach. The analysis of existence and uniqueness of solutions to the linear programming formulation for fixed controls represents the first contribution of this work. Then, an approximate scheme for the linear programming formulations is established. To this end, a novel discretization of the involved measures and constraints using finite dimensional function subspaces is introduced. Its convergence is proven using weak convergence of measures, and a detailed analysis of the approximate relaxed controls. The applicability of the established method is shown through a collection of examples from stochastic control. The considered examples include models with bounded or unbounded state space, models featuring continuous and singular control as well as discounted or long-term average cost criteria. Analyses of various model parameters are given, and in selected examples, the approximate solutions are compared to available analytic solutions. A summary and an outlook on possible research directions is given.
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
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a The University of Wisconsin - Milwaukee. $b Mathematics. $3 1188708
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10815046 $z click for full text (PQDT)