Lévy Processes

Information

In this reading group we will be make use the following two books:

  • "Lévy Processes and Stochastic Calculus" (Second Edition) by David Applebaum
  • "Fluctuations of Lévy Processes with Applications" by Andreas E. Kyprianou

The schedule lists the material that participants are suggested to read before each session. Members of the reading group are encouraged to participate in presenting the material.

We are using Teams to conduct the session. Here is the link to the meeting. Please email me or Terence if you've signed up and haven't been added to the team.

Prequisites

A basic knowledge of measure and probability theory is needed. The material in Section 1.1 of Lévy Processes and Stochastic Calculus serves as a good review of these topics. Familiarity with Brownian motion is helpful but not essential.

Accessing the reading material

"Lévy Processes and Stochastic Calculus" by David Applebaum can be accessed online in a PDF format if you have an Oxford Single Sign-On. Please follow these steps:

  1. Press the "Log in" button on the top right of this page
  2. Choose "Log in via Shibboleth or Athens"
  3. Select "University of Oxford" as the organization
  4. Sign in using your Oxford Single Sign-On details

Below each chapter there should now be a green checkmark with "Access" written next to it. Click on PDF to access the file for each chapter.

"Fluctuations of Lévy Processes with Applications" by Andreas E. Kyprianou can be accessed here using an Oxford Single Sign-On.

Sign up

Please sign up using the form here. Alternatively you can email an organiser using the contact details below.

Contact us

This reading group is co-organised by Terence Tsui and Zheneng Xie of the Oxford University Statistics Department. Please contact us at xie@maths.ox.ac.uk or terence.tsui@maths.ox.ac.uk if there are any questions. We also welcome suggestions or other feedback. Feedback can also be submitted anonymously here.

Schedule

Sessions are on Friday from 11:00 to 12:00 BST starting Week 2 on Jan 25

The following information can also be found in this Google Calendar. Note this schedule is subject to change depending on progress in the actual sessions.

WeekDateReading MaterialTopic
207/05"Lévy Processes and Stochastic Calculus" Pages 99--112Jumps of a Lévy process: Poisson random measures
314/05"Lévy Processes and Stochastic Calculus" Pages 113--131Lévy--Itô decomposition
421/05"Lévy Processes and Stochastic Calculus" Pages 113--131Lévy--Itô decomposition
528/05"Fluctations of Lévy Processes with Applications" Chapter 6Wiener--Hopf factorisation
604/06"Fluctations of Lévy Processes with Applications" Chapter 6Wiener--Hopf factorisation
711/06Lévy trees
818/06Lévy trees
© 2024 Zheneng Xie. All Rights Reserved.