Sonny completed a Bachelor’s in Actuarial Sciences at the National Autonomous University of Mexico where he was interested in statistics and especially in survey sampling. He then did a Master’s in Probability and Statistics at the Center for Research in Mathematics (CIMAT) in Guanajuato Mexico, where he developed curiosity in stochastic Actuarial Risk models and later graduated with a thesis on the Gerber-Shiu function for a renewal risk model with positive jumps and diffusion perturbation. His professional experience includes working as a statistical consultant for the public sector of arts and culture. He enjoys playing the flute, listening to chamber music and doing road cycling.

Research project title:
Excursions from Hyperplanes for Isotropic Stable Processes

Supervisor(s):
Andreas Kyprianou, Alex Cox, Juan Carlos Pardo Millan

Project description:
Breaking the paths of isotropic Lévy processes in Rᵈ in radial excursions from the origin is a technique that has been used to understand the behaviour of processes when they approach the origin or the unit sphere S ={x ∈ Rᵈ : | x | = 1 }. We aim to build on these ideas and techniques and consider related behaviour in relation to the hyperplane H = {x ∈ Rᵈ: <x, v> =0 }, with v ∈ S, and use the associated path decomposition to address questions such as how to condition the process to stay on one side of the hyperplane, examining the point of closest reach to H, conditioning to never touch the hyperplane or the relationship between this and the spherical case via conformal transformations of Riemannian manifolds.