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Dan Crisan

Professor of Mathematics

Imperial College London

Department of Mathematics

180 Queen's Gate

London SW7 2AZ, UK

d.crisan@imperial.ac.uk

0207 594 8489

Stochastic Analysis Group

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Welcome to Dan Crisan's Homepage

I am currently a Professor of Mathematics in the Department of Mathematics at Imperial College London, where I also serve as Director of the EPSRC Centre for Doctoral Training in the Mathematics for our Future Climate: Theory, Data and Simulation (MFC CDT) (mfccdt.ac.uk).

The MFC CDT is a four-year, interdisciplinary PhD programme that harnesses mathematical theory, data, and simulation to address urgent challenges posed by climate change. It is jointly run by Imperial College London, the University of Reading, and the University of Southampton, working closely with partners across weather services, research institutions, business and industry, charities, and government. The programme offers fully funded PhD studentships. For more information about the MFC CDT, including the programme structure and how to apply, please visit mfccdt.ac.uk. In addition to my teaching and supervisory activities, I am one of the four Principal Investigators on the project Stochastic Transport in Upper Ocean Dynamics, a large-scale collaboration advancing our understanding of how randomness and turbulence shape the transport of heat, tracers, and pollutants in the oceans. This project has been awarded a prestigious six-year ERC Synergy Grant.

My long-term research interests lie broadly in Stochastic Analysis, a branch of mathematics concerned with understanding and modelling systems that evolve under the influence of randomness and uncertainty. Applications range from climate and geophysical fluid dynamics to finance and engineering.

To get an idea of my current research interests, here are some papers:

• Stochastic PDEs

o Well-Posedness for the Euler-Boussinesq equation with Stochastic Transport Noise. D Crisan, D Holm, P Korn
o Local well-posedness for the great lake equation with transport noise D Crisan, O Lang arXiv preprint arXiv:2003.03357
o 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:1907.11884
o 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:2101.11460
o 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:1905.03524
o 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:1907.11884
o 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:2008.07803
o 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:2101.03957
o 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:1703.04177
o D Crisan, J Miguez, Nested particle filters for online parameter estimation in discrete-time state-space Markov models, arXiv preprint arXiv:1308.1883
o D Crisan, J Houssineau, A Jasra, Unbiased Multi-index Monte Carlo, arXiv preprint arXiv:1702.03057
o D Paulin, A Jasra, D Crisan, A Beskos, Optimization Based Methods for Partially Observed Chaotic Systems, arXiv preprint arXiv:1702.02484

• Fluid Dynamics
  • Theoretical and computational analysis of the thermal quasi-geostrophic model, D Crisan, DD Holm, E Luesink, PR Mensah, W Pan. Journal of nonlinear science 33 (5), 96. 2023. (journal link)
  • An Implementation of Hasselmann’s Paradigm for Stochastic Climate Modelling, D. Crisan, D.D. Holm & P. Korn. 2023.(journal link)
  • Variational principles for fluid dynamics on rough paths — D. Crisan, D.D. Holm, J.M. Leahy, T. Nilssen. Advances in Mathematics, 2022. (journal link)
  • Semi-martingale driven variational principles — O.D. Street, D. Crisan. Proceedings of the Royal Society A, 2021. (journal link)
  • Wave breaking for the Stochastic Camassa–Holm equation — D. Crisan, D.D. Holm. Physica D, 376:138–143, 2018. (journal link)
• Stochastic PDEs
  • Well-posedness properties for a stochastic rotating shallow water model — D. Crisan & O. Lang. *Journal of Dynamics and Differential Equations*, 2023. (doi link)
  • Noise calibration for the stochastic rotating shallow water model — D. Crisan, O. Lang, A. Lobbe, P.J. van Leeuwen & R. Potthast. *Journal of Mathematical Fluid Mechanics*, 25:29, 2023. (doi link)
  • Analytical Properties for a Stochastic Rotating Shallow Water Model Under Location Uncertainty — O. Lang, D. Crisan & É. Mémin. 2023.
  • Solution properties of a 3D stochastic Euler fluid equation — D. Crisan, F. Flandoli, D.D. Holm. Journal of Nonlinear Science, 29(3):813–870, 2019. (doi link)
• Particle Representations / Approximations to (Stochastic) PDEs
  • 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. 2022.
  • Cubature on Wiener space for McKean–Vlasov SDEs with smooth scalar interaction — D. Crisan, E. McMurray. Annals of Applied Probability, 29(1):130–177, 2019.
  • Two-dimensional pseudo-gravity model — J. Barré, D. Crisan, T. Goudon. Transactions of the AMS, 371(4):2923–2962, 2019.
  • Numerical method for FBSDEs of McKean–Vlasov type — J.F. Chassagneux, D. Crisan, F. Delarue. Annals of Applied Probability, 29(3):1640–1684, 2018.
  • Unbiased multi-index Monte Carlo — D. Crisan, J. Houssineau, A. Jasra. Stochastic Analysis and Applications, 36(2):257–273, 2018.
  • Nested particle filters for online parameter estimation — D. Crisan, J. Míguez. Bernoulli, 24(4A):3039–3086, 2018.
  • Particle representations for SPDEs with boundary conditions — D. Crisan, C. Janjigian, T.G. Kurtz. Electronic Journal of Probability, 23:1–32, 2018.
• Nonlinear Filtering
  • Pathwise approximations for the solution of the non-linear filtering problem — D. Crisan, A. Lobbe, S. Ortiz-Latorre. In *Stochastic Analysis, Filtering and Stochastic Optimization* (commemorative volume to Mark H. A. Davis), 2022.
  • A high-order time discretization of the solution of the non-linear filtering problem — D. Crisan, S. Ortiz-Latorre. Stochastics and PDEs: Analysis and Computation, 2019.
• Other (Recent & Preprints)
  • Data assimilation for the stochastic Camassa–Holm equation using particle filtering: a numerical investigation — C.J. Cotter, D. Crisan & M.K. Singh. arXiv:2402.06927, 2024.
  • Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization — Ö.D. Akyildiz, D. Crisan, J. Míguez. Statistics and Computing, 30(6):1645–1663, 2020.
  • Data assimilation for a quasi-geostrophic model with circulation-preserving stochastic transport noise — C. Cotter, D. Crisan, D. Holm, W. Pan & I. Shevchenko. Journal of Statistical Physics, 179:1186–1221, 2020.

In addition, I completed a joint project with Colin Cotter and Darryl Holm, devoted to the development of rigorously validated Data Assimilation methodologies for high–dimensional systems. The project was funded by an EPSRC grant.

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