Mehar graduated with an MSci in Mathematics from University College London in 2020. During his time there he developed a particular interest in probability theory, and wrote his Master’s project on reinforced random walks. He is interested in pursuing probability and stochastic analysis further, as well as exploring their various connections to fields such as financial mathematics. Outside of Maths, he enjoys reading and cooking.

Research project title:
Problems for self-similar Markov processes

Supervisor(s):
Andreas Kyprianou, Alex Cox

Project description:
The interplay between stable Lévy processes and self-similar Markov processes has attracted much interest in recent decades, and is what continues to motivate research in the field of Lévy processes. In particular, the problem of characterising the laws of Markov processes via Doob h-transforms which arise from limiting procedures of conditioned processes has been considered. As part of this project, we aim to describe the Markov Additive Process conditioned to continuously hit the unit sphere in d dimensions, building upon existing work which involved conditioning the stable process to continuously approach the unit sphere.