I am currently Professor of Mathematics at the Department of Mathematics of Imperial College London and Director of the EPSRC Centre for Doctoral Training in the Mathematics of Planet Earth http://mpecdt.org/. My long-term research interests lie broadly in Stochastic Analysis, a branch of Mathematics that looks at understanding and modelling systems that behave randomly.
I am one of the four PIs of the project Stochastic Transport in Upper Ocean Dynamics .
This project has received a six year Synergy ERC award.
Lecture on Particle Filters
Particle Filters for Data Assimilation
Big data, data assimilation, and uncertainty quantification
The Mathematics of Climate and the Environment
IHP, Paris, September 9 - December 21 2019
To get an idea of my current research interests, here are some recent papers:
• Fluid Dynamics
o Pathwise approximations for the solution of the non-linear filtering problem D Crisan, A Lobbe, S Ortiz-Latorre arXiv preprint arXiv:2101.03957o Variational principles for fluid dynamics on rough paths D Crisan, DD Holm, JM Leahy, T Nilssen arXiv preprint arXiv:2004.07829o Semi-martingale driven variational principles OD Street, D Crisan arXiv preprint arXiv:2001.10105
• Stochastic PDEs
o Well-Posedness for the Euler-Boussinesq equation with Stochastic Transport Noise. D Crisan, D Holm, P Korno Local well-posedness for the great lake equation with transport noise D Crisan, O Lang arXiv preprint arXiv:2003.03357o A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equation C Cotter, D Crisan, DD Holm, W Pan, I Shevchenko arXiv preprint arXiv:1907.11884o D. Crisan, DD Holm, Wave breaking for the Stochastic Camassa-Holm equation, arXiv preprint arXiv:1707.09000 o D Crisan, F Flandoli, DD Holm, Solution properties of a 3D stochastic Euler fluid equation, arXiv preprint arXiv:1704.06989
• Particle representations/approximations to (stochastic) PDEs
o Log-Normalization Constant Estimation using the Ensemble Kalman-Bucy Filter with Application to High-Dimensional Models D Crisan, P Del Moral, A Jasra, H Ruzayqat arXiv preprint arXiv:2101.11460o Uniform in time estimates for the weak error of the Euler method for SDEs and a Pathwise Approach to Derivative Estimates for Diffusion Semigroups D Crisan, P Dobson, M Ottobre arXiv preprint arXiv:1905.03524o A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equation C Cotter, D Crisan, DD Holm, W Pan, I Shevchenko arXiv preprint arXiv:1907.11884o Score-Based Parameter Estimation for a Class of Continuous-Time State Space Models A Beskos, D Crisan, A Jasra, N Kantas, H Ruzayqat arXiv preprint arXiv:2008.07803o J Barre, D Crisan, T Goudon, Two-dimensional pseudo-gravity model, arXiv preprint arXiv:1610.01296 o D Crisan, C Janjigian, TG Kurtz, Particle representations for stochastic partial differential equations with boundary conditions, arXiv preprint arXiv:1607.08909
• Nonlinear filtering
o Pathwise approximations for the solution of the non-linear filtering problem D Crisan, A Lobbe, S Ortiz-Latorre arXiv preprint arXiv:2101.03957o D Crisan, S Ortiz-Latorre, A high order time discretization of the solution of the non-linear filtering problem, arXiv preprint arXiv:1711.08012
• Forward Backward Differential Equations
o JF Chassagneux, D Crisan, F Delarue, Numerical Method for FBSDEs of McKean-Vlasov Type arXiv preprint arXiv:1703.02007
• Probabilistic Numerical Methods (including MC, SMC, Particle Filters)
o D Crisan, E McMurray, Cubature on Wiener Space for McKean-Vlasov SDEs with Smooth Scalar Interaction, arXiv preprint arXiv:1703.04177o D Crisan, J Miguez, Nested particle filters for online parameter estimation in discrete-time state-space Markov models, arXiv preprint arXiv:1308.1883o D Crisan, J Houssineau, A Jasra, Unbiased Multi-index Monte Carlo, arXiv preprint arXiv:1702.03057o D Paulin, A Jasra, D Crisan, A Beskos, Optimization Based Methods for Partially Observed Chaotic Systems, arXiv preprint arXiv:1702.02484