Luis Mario Chaparro Jáquez

Research introduction

I am interested in stochastic analysis and numerical analysis with strong links to partial differential equations. My PhD thesis dealt with the theoretical analysis of SDEs and McKean-Vlasov SDEs with distributional coefficients and numerical implementations for them, you can find my thesis in the White Rose eTheses Online repository.

Because of this, I naturally gravitate around SDEs with irregular coefficients in general. My main concern is to find results about the convergence rates numerical methods for said SDEs. Additionally, I am passionate about numerical analysis and the implementations of numerical schemes for such SDEs, the latter which is not always entertained by the literature where convergence of the scheme itself is studied. This is, in my opinion, reasonable; since very often the results on convergence rates are found in order to justify the use of popular numerical schemes like the Euler-Maruyama and Milstein methods, without changes. Hence, an implementation of the Euler-Maruyama scheme for an article where somebody proofs that the Euler-Maruyama scheme works just as it has always worked is very uninteresting. However, there are often SDEs which require a more dedicated approach, it obviously comes to mind the case of SDEs wiht distributional drifts; because you cannot evaluate a distribution point-wise, but this is also present in the case of some SDEs with functional drifts.

List of publications

Selected events and materials

Teaching