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Singular Stochastic Differential Equ...

Nam, Kyeongsik.

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Singular Stochastic Differential Equations with Elliptic and Hypoelliptic Diffusions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Singular Stochastic Differential Equations with Elliptic and Hypoelliptic Diffusions./
Author:	Nam, Kyeongsik.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	77 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-04, Section: B.
Contained By:	Dissertations Abstracts International82-04B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27744653
ISBN:	9798678170996

Singular Stochastic Differential Equations with Elliptic and Hypoelliptic Diffusions.
Nam, Kyeongsik.

Singular Stochastic Differential Equations with Elliptic and Hypoelliptic Diffusions. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 77 p.

Source: Dissertations Abstracts International, Volume: 82-04, Section: B.

Thesis (Ph.D.)--University of California, Berkeley, 2020.

This item must not be sold to any third party vendors.

In this thesis, the well-posedness of stochastic differential equations (SDEs) with singular coefficients is discussed. First, it is proved that SDEs with elliptic diffusion possess a unique solution when drift vector fields belong to the Orlicz-critical space. Then, it is shown that SDEs with degenerate and hypoelliptic diffusion are well-posed for a large class of singular drifts. A basic theory on Lorentz spaces and the analysis on the homogeneous Carnot group will also be introduced.

ISBN: 9798678170996Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Homogeneous group

Singular Stochastic Differential Equations with Elliptic and Hypoelliptic Diffusions.
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100 1 $a Nam, Kyeongsik. $3 3558891
245 1 0 $a Singular Stochastic Differential Equations with Elliptic and Hypoelliptic Diffusions.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 77 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-04, Section: B.
500 $a Advisor: Rezakhanlou, Fraydoun.
502 $a Thesis (Ph.D.)--University of California, Berkeley, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a In this thesis, the well-posedness of stochastic differential equations (SDEs) with singular coefficients is discussed. First, it is proved that SDEs with elliptic diffusion possess a unique solution when drift vector fields belong to the Orlicz-critical space. Then, it is shown that SDEs with degenerate and hypoelliptic diffusion are well-posed for a large class of singular drifts. A basic theory on Lorentz spaces and the analysis on the homogeneous Carnot group will also be introduced.
590 $a School code: 0028.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Homogeneous group
653 $a Hypoelliptic operator
653 $a Lorentz space
653 $a Stochastic differential equation
690 $a 0405
690 $a 0642
710 2 $a University of California, Berkeley. $b Mathematics. $3 1685396
773 0 $t Dissertations Abstracts International $g 82-04B.
790 $a 0028
791 $a Ph.D.
792 $a 2020
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27744653