Stochastic Equations Driven by Lévy Processes

Author (Researcher Name)

Sayantan Maitra Dr., Indian Statistical Institute

Date of Submission

July 2022

Date of Award

7-1-2023

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Mathematics

Department

Theoretical Statistics and Mathematics Unit (TSMU-Bangalore)

Supervisor

Athreya, Siva (TSMU-Bangalore; ISI)

Abstract (Summary of the Work)

In this thesis we first study a stochastic heat equation driven by Lévy noise and understand the well-posedness of the associated martingale problem. We use the method of duality to establish the same. In the second part of the thesis we explore the method of Algebraic duality and establish weak-uniqueness for a class of infinite dimensional interacting diffusions. We conclude the thesis with some preliminary observations on how to construct path wise stochastic integrals under a Poisson random measure

Comments

ProQuest Collection ID: https://www.proquest.com/pqdtlocal1010185/dissertations/fromDatabasesLayer?accountid=27563

Control Number

ISILib-TH

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

Recommended Citation

Maitra, Sayantan Dr., "Stochastic Equations Driven by Lévy Processes" (2023). Doctoral Theses. 526.
https://digitalcommons.isical.ac.in/doctoral-theses/526