Course on Martingale problem and lumpability for Markov processes

A one month course by Johel Beltrán, Pontificia Universidad Católica del Perú, with sessions Mon, Wed, Thu, from 14:00 to 16:00, February 18 to March 14 2019. Room 5.18, Mathematics Building on the IST Alameda campus.

The martingale problem is an important tool in probability theory introduced by Stroock and Varadhan as an approach to Markov processes. The purpose of this course is to present a detailed introduction to the martingale problem theory as well as a review of recent applications to the study of two different subjects:

  1. metastability of zero range processes and
  2. Kingman’s process as scaling limit for coalescing random walks.

Interestingly, they both will be tackled as instances of a more general problem: lumpability for Markov processes.