Paul Dobson


Paul Dobson

PhD student
School of Mathematics and Computer Sciences at Heriot-Watt University
School of Mathematics at University of Edinburgh
Maxwell Institute for Mathematical Sciences, Edinburgh

Mailing address:
School of Mathematical & Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK

Office: Room F.15, Colin Maclaurin Building
E-mail: pd14(at)hw.ac.uk

Research Interests: My main interest area is Stochastic analysis, and in particular the interplay between stochastic analysis and functional analysis. More precisely, my interests include:
  • Degenerate Diffusion processes
  • Stochastic Representations of solutions to parabolic PDEs
  • SDE theory
  • Theory of Markov semigroups
  • Malliavin calculus
  • Geometric control theory
  • Ergodic Theory


Publications/Work in progress:
  1. Long-time behaviour of Degenerate diffusions: UFG-type SDE and time-inhomogeneous hypoelliptic processes (with T. Cass, D. Crisan, M. Ottobre) submitted to Annals of Probability also available on arXiv at https://arxiv.org/abs/1805.01350.
  2. Uniform in time convergence for the Euler method and a Pathwise Approach to Derivative Estimates for Diffusion Semigroups (with D. Crisan and M. Ottobre) submitted to transactions of the AMS also available on arXiv at https://arxiv.org/abs/1905.03524.
  3. Comparison of some reversible and non-reversible sampling schemes (with I. Fursov, G. Lord and M. Ottobre) submitted to Foundations of Data Science also available on arXiv at https://arxiv.org/abs/1903.06960.


Teaching: I have been a teaching assistant for the following courses:
  • Multivariable Calculus and Real Analysis A (Autumn 2018)
  • Multivariable Calculus and Real Analysis B (Spring 2019)
  • Discrete Mathematics (Spring 2018)
  • Numerical Analysis C (Autumn 2017)
  • Optimisation (Autumn 2017)
  • Optimisation (Autumn 2017)
  • Mathematics for Engineers and Scientists 2 (Spring 2017 and 2018)
  • Mathematics for Engineers and Scientists 3 (Autumn 2016)