$dX_t = b(X_t)\,dt + \sigma(X_t)\,dW_t$
Stochastic Analysis
Itô calculus, stochastic differential equations and the behaviour of processes driven by noise.
PhD Student
Oliver Nash
Department of Mathematics, Imperial College London
PhD Thesis Inference and inverse problems for stochastic interacting particle systems
I work where probability meets partial differential equations. My research centres on stochastic interacting particle systems: their analysis, their numerical simulation, and how to draw statistical inferences about them from data. Currently funded by CCMI CDT.
Research Interests
Randomness, differential equations, and the computation in between.
$\hat{\theta}_n \longrightarrow \theta$
Statistical Inference
Estimating parameters and quantifying uncertainty in random models from discrete, noisy observations.
$\mathbb{E}[f(X_t)\mid \mathcal{F}_s]$
Machine Learning for Stochastic Processes
Developing data-driven methods for learning, forecasting and uncertainty quantification in systems governed by stochastic dynamics.
$\partial_t u = \Delta u + f(u)$
Applied PDE Theory
Well-posedness, regularity and qualitative behaviour of partial differential equations arising in applications.
$u^{n+1} = u^n + \Delta t\, F(u^n)$
Numerical Methods
Designing and analysing discretisation schemes: convergence, stability and computational cost.
Projects
Things I am building and working on.
Field of Streams
Simulation schemes for stochastic differential equations and stochastic PDEs: methods for generating accurate sample paths of systems driven by noise.