Functional inequalities and convergence of stochastic processes
Pedrotti F. 2024. Functional inequalities and convergence of stochastic processes. Institute of Science and Technology Austria.
Download
Thesis
| PhD
| Published
| English
Author
Supervisor
Department
Series Title
ISTA Thesis
Abstract
This thesis deals with the study of stochastic processes and their ergodicity properties. The
variety of problems encountered calls for a set of different approaches, ranging from classical to
modern ones: a special place is held by probabilistic methods based on couplings, by functional
inequalities, and by the theory of gradient flows in the space of measures.
The material is organized as follows. Chapter 1 contains the introduction to this thesis, starting
with a general presentation of some of the relevant topics. Section 1.1 is dedicated to the
theory of gradient flows in metric spaces, and introduces the first contribution of this thesis
[DSMP24], which is presented in detail in Chapter 2. Section 1.2 moves to the topic of
curvature of Markov chains, concluding with a brief description of our second contribution
[Ped23], which is included in Chapter 3. Section 1.3 discusses applications of stochastic
processes to the theory of sampling, in particular the recent framework of score-based diffusion
models, and our contribution [PMM24], which is contained in Chapter 4. Section 1.4 discusses
some related problems, concerning the regularization properties of the heat flow. It serves
as a motivation for the work [BP24], which we report in Chapter 5. Finally, Section 1.5
discusses the last contribution of this thesis, which can be found in Chapter 6. It deals with
the convergence to equilibrium of a particular stochastic model from quantitative genetics:
this is established via some functional inequalities, which we prove with probabilistic arguments
based on couplings.
Publishing Year
Date Published
2024-07-31
Page
183
ISSN
IST-REx-ID
Cite this
Pedrotti F. Functional inequalities and convergence of stochastic processes. 2024. doi:10.15479/at:ista:17336
Pedrotti, F. (2024). Functional inequalities and convergence of stochastic processes. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:17336
Pedrotti, Francesco. “Functional Inequalities and Convergence of Stochastic Processes.” Institute of Science and Technology Austria, 2024. https://doi.org/10.15479/at:ista:17336.
F. Pedrotti, “Functional inequalities and convergence of stochastic processes,” Institute of Science and Technology Austria, 2024.
Pedrotti F. 2024. Functional inequalities and convergence of stochastic processes. Institute of Science and Technology Austria.
Pedrotti, Francesco. Functional Inequalities and Convergence of Stochastic Processes. Institute of Science and Technology Austria, 2024, doi:10.15479/at:ista:17336.
All files available under the following license(s):
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0):
Main File(s)
File Name
thesis_final.pdf
2.94 MB
Access Level
![Open access file OA](https://research-explorer.ista.ac.at/images/access_open.png)
Date Uploaded
2024-08-02
MD5 Checksum
11650bab714ef85ad43a287060850523
Source File
File Name
thesis_final_source.zip
6.29 MB
Access Level
![Restricted access for author/reviewer only. Restricted](https://research-explorer.ista.ac.at/images/access_restricted.png)
Date Uploaded
2024-08-02
MD5 Checksum
c30ba5611941226cf1bfc867c25b1e80
Material in ISTA:
Part of this Dissertation
Part of this Dissertation
Part of this Dissertation
Part of this Dissertation
Part of this Dissertation