---
OA_place: publisher
_id: '17336'
abstract:
- lang: eng
  text: "This thesis deals with the study of stochastic processes and their ergodicity
    properties. The\r\nvariety of problems encountered calls for a set of different
    approaches, ranging from classical to\r\nmodern ones: a special place is held
    by probabilistic methods based on couplings, by functional\r\ninequalities, and
    by the theory of gradient flows in the space of measures.\r\n\r\nThe material
    is organized as follows. Chapter 1 contains the introduction to this thesis, starting\r\nwith
    a general presentation of some of the relevant topics. Section 1.1 is dedicated
    to the\r\ntheory of gradient flows in metric spaces, and introduces the first
    contribution of this thesis\r\n[DSMP24], which is presented in detail in Chapter
    2. Section 1.2 moves to the topic of\r\ncurvature of Markov chains, concluding
    with a brief description of our second contribution\r\n[Ped23], which is included
    in Chapter 3. Section 1.3 discusses applications of stochastic\r\nprocesses to
    the theory of sampling, in particular the recent framework of score-based diffusion\r\nmodels,
    and our contribution [PMM24], which is contained in Chapter 4. Section 1.4 discusses\r\nsome
    related problems, concerning the regularization properties of the heat flow. It
    serves\r\nas a motivation for the work [BP24], which we report in Chapter 5. Finally,
    Section 1.5\r\ndiscusses the last contribution of this thesis, which can be found
    in Chapter 6. It deals with\r\nthe convergence to equilibrium of a particular
    stochastic model from quantitative genetics:\r\nthis is established via some functional
    inequalities, which we prove with probabilistic arguments\r\nbased on couplings.\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Francesco
  full_name: Pedrotti, Francesco
  id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
  last_name: Pedrotti
citation:
  ama: Pedrotti F. Functional inequalities and convergence of stochastic processes.
    2024. doi:<a href="https://doi.org/10.15479/at:ista:17336">10.15479/at:ista:17336</a>
  apa: Pedrotti, F. (2024). <i>Functional inequalities and convergence of stochastic
    processes</i>. Institute of Science and Technology Austria. <a href="https://doi.org/10.15479/at:ista:17336">https://doi.org/10.15479/at:ista:17336</a>
  chicago: Pedrotti, Francesco. “Functional Inequalities and Convergence of Stochastic
    Processes.” Institute of Science and Technology Austria, 2024. <a href="https://doi.org/10.15479/at:ista:17336">https://doi.org/10.15479/at:ista:17336</a>.
  ieee: F. Pedrotti, “Functional inequalities and convergence of stochastic processes,”
    Institute of Science and Technology Austria, 2024.
  ista: Pedrotti F. 2024. Functional inequalities and convergence of stochastic processes.
    Institute of Science and Technology Austria.
  mla: Pedrotti, Francesco. <i>Functional Inequalities and Convergence of Stochastic
    Processes</i>. Institute of Science and Technology Austria, 2024, doi:<a href="https://doi.org/10.15479/at:ista:17336">10.15479/at:ista:17336</a>.
  short: F. Pedrotti, Functional Inequalities and Convergence of Stochastic Processes,
    Institute of Science and Technology Austria, 2024.
corr_author: '1'
das_tickbox: '0'
date_created: 2024-07-29T09:14:14Z
date_published: 2024-07-31T00:00:00Z
date_updated: 2026-10-02T12:22:41Z
day: '31'
ddc:
- '500'
- '510'
- '515'
- '519'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JaMa
doi: 10.15479/at:ista:17336
doi_confirm: '1'
ec_funded: 1
file:
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  creator: fpedrott
  date_created: 2024-08-02T09:23:26Z
  date_updated: 2024-08-02T09:23:26Z
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  date_created: 2024-08-02T09:27:15Z
  date_updated: 2024-08-02T09:27:15Z
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file_date_updated: 2024-08-02T09:27:15Z
fulldoi: https://doi.org/10.15479/at:ista:17336
has_accepted_license: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '07'
oa: 1
oa_version: Published Version
page: '183'
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '716117'
  name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
publication_identifier:
  issn:
  - 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
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researchdata_availability: no
status: public
supervisor:
- first_name: Jan
  full_name: Maas, Jan
  id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
  last_name: Maas
  orcid: 0000-0002-0845-1338
supplementarymaterial: no
title: Functional inequalities and convergence of stochastic processes
tmp:
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  legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
  name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
    (CC BY-NC-ND 4.0)
  short: CC BY-NC-ND (4.0)
type: dissertation
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
year: '2024'
...