- Title Information
- Title
- Brownian motion on homogeneous space and control systems via Riemannian submersion using mean curvature drift
- Type of Resource (primo)
- dissertations
- Name:
Personal
- Name Part
- Huang, Ching-Peng
- Role
- Role Term:
Text
- creator
- Name:
Personal
- Name Part
- Hassett, Brendan
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Menon, Govind
- Role
- Role Term:
Text
- Advisor
- Name:
Personal
- Name Part
- Darbon, Jérôme
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Department of Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Origin Information
- Copyright Date
- 2022
- Physical Description
- Extent
- vi, 48 p.
- digitalOrigin
- born digital
- Note:
thesis
- Thesis (Ph. D.)--Brown University, 2022
- Genre (aat)
- theses
- Abstract
- We begin by asking how to write down Brownian motion on certain quotient
Riemannian manifolds. The projection formula for the Laplace-Beltrami operator through Riemannian submersions indicates the Brownian motion on the total
space gains a drift term from the mean curvature flow of fibers through the submersion.
With this key fact, in the first chapter, we write down formula for Brownian motion on several Riemannian homogeneous spaces, in particular symmetric
spaces, using their common embedding coordinates in matrix form. Moreover,
we study the Bures-Wasserstein geometry on positive semidefinite matrices and
write down a formula of its Brownian motion via computing the aforementioned
mean curvature flow.
In the second chapter, we investigate the idea of utilizing the mean curvature
flow on the Bures-Wasserstein geometry by altering the metric, deriving a Lie theoretical invariant control system
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/01133519")
- Topic
- Stochastic processes
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00940940")
- Topic
- Geometry, Riemannian
- Subject (fast)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/00998135")
- Topic
- Lie groups
- Subject
- Topic
- control system
- Subject
- Topic
- random matrix
- Language
- Language Term (ISO639-2B)
- English
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20220706