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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



Publications

Submitted
1. D Crisan, S Ortiz-Latorre, A high order time discretization of the solution of the non-linear filtering problem, arXiv preprint arXiv:1711.08012
2. D. Crisan, DD Holm, Wave breaking for the Stochastic Camassa-Holm equation, arXiv preprint arXiv:1707.09000
3. D Crisan, F Flandoli, DD Holm, Solution properties of a 3D stochastic Euler fluid equation, arXiv preprint arXiv:1704.06989
4. D Crisan, E McMurray, Cubature on Wiener Space for McKean-Vlasov SDEs with Smooth Scalar Interaction, arXiv preprint arXiv:1703.04177
5. JF Chassagneux, D Crisan, F Delarue, Numerical Method for FBSDEs of McKean-Vlasov Type arXiv preprint arXiv:1703.02007
6. D Crisan, J Houssineau, A Jasra, Unbiased Multi-index Monte Carlo, arXiv preprint arXiv:1702.03057
7. D Paulin, A Jasra, A Beskos, D Crisan, A 4D-Var Method with Flow-Dependent Background Covariances for the Shallow-Water Equations, arXiv preprint arXiv:1710.11529
8. D Paulin, A Jasra, D Crisan, A Beskos, Optimization Based Methods for Partially Observed Chaotic Systems, arXiv preprint arXiv:1702.02484
9. J Barre, D Crisan, T Goudon, Two-dimensional pseudo-gravity model, arXiv preprint arXiv:1610.01296
10. D Paulin, A Jasra, D Crisan, A Beskos, On Concentration Properties of Partially Observed Chaotic Systems, arXiv preprint arXiv:1608.08348
11. D Crisan, J Miguez, Nested particle filters for online parameter estimation in discrete-time state-space Markov models, arXiv preprint arXiv:1308.1883
12. D Crisan, C Janjigian, TG Kurtz, Particle representations for stochastic partial differential equations with boundary conditions, arXiv preprint arXiv:1607.08909
Published
13. D Crisan, J Miguez, Uniform convergence over time of a nested particle filtering scheme for recursive parameter estimation in state--space Markov models, arXiv preprint arXiv:1603.09005, Adv. Appl. Prob. 49, 1170–1200 2017.
14. D Crisan, E McMurray, Smoothing properties of McKean–Vlasov SDEs, Probability Theory and Related Fields, 1-52, 2017.
15. Beskos, Alexandros; Crisan, Dan; Jasra, Ajay; Kamatani, Kengo; Zhou, Yan; A stable particle filter for a class of high-dimensional state-space models. Adv. in Appl. Probab. 49 (2017), no. 1, 24–48.
16. D Crisan, M Ottobre, Pointwise gradient bounds for degenerate semigroups (of UFG type) Proc. R. Soc. A 472, 2016.
17. Crisan, Dan; Litterer, Christian; Lyons, Terry Kusuoka-Stroock gradient bounds for the solution of the filtering equation. J. Funct. Anal. 268 (2015), no. 7, 1928–1971.
18. Crisan, Dan; Otobe, Yoshiki; Peszat, Szymon Inverse problems for stochastic transport equations. Inverse Problems 31 (2015), no. 1, 015005, 20 pp.
19. D. Crisan, The stochastic filtering problem: a brief historical account, Volume 51, Issue A (Celebrating 50 Years of The Applied Probability Trust), December 2014 , pp. 13-22.
10. Cass, Thomas; Clark, Martin; Crisan, Dan The filtering equations revisited. Stochastic analysis and applications 2014, 129–162, Springer Proc. Math. Stat., 100, Springer, Cham, 2014.
21. Crisan, Dan; Míguez, Joaquín Particle-kernel estimation of the filter density in state-space models. Bernoulli 20 (2014), no. 4, 1879–1929.
22. Crisan, Dan; Kurtz, Thomas G.; Lee, Yoonjung Conditional distributions, exchangeable particle systems, and stochastic partial differential equations. Ann. Inst. Henri Poincaré Probab. Stat. 50 (2014), no. 3, 946–974.
23. Crisan, Dan; Xiong, Jie Numerical solution for a class of SPDEs over bounded domains. Stochastics 86 (2014), no. 3, 450–472.
24. Beskos, Alexandros; Crisan, Dan; Jasra, Ajay On the stability of sequential Monte Carlo methods in high dimensions. Ann. Appl. Probab. 24 (2014), no. 4, 1396–1445.
25. Beskos, Alexandros; Crisan, Dan O.; Jasra, Ajay; Whiteley, Nick Error bounds and normalising constants for sequential Monte Carlo samplers in high dimensions. Adv. in Appl. Probab. 46 (2014), no. 1, 279–306.
26. Chassagneux, Jean-François; Crisan, Dan Runge-Kutta schemes for backward stochastic differential equations. Ann. Appl. Probab. 24 (2014), no. 2, 679–720.
27. Chassagneux, Jean-François; Crisan, Dan Runge-Kutta schemes for backward stochastic differential equations. Ann. Appl. Probab. 24 (2014), no. 2, 679–720. 26. Crisan, Dan; Manolarakis, Konstantinos Second order discretization of backward SDEs and simulation with the cubature method. Ann. Appl. Probab. 24 (2014), no. 2, 652–678.
28. Crisan, D.; Diehl, J.; Friz, P. K.; Oberhauser, H. Robust filtering: correlated noise and multidimensional observation. Ann. Appl. Probab. 23 (2013), no. 5, 2139–2160.
29. Crisan, Dan; Ortiz-Latorre, Salvador A Kusuoka-Lyons-Victoir particle filter. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 469 (2013), no. 2156, 20130076, 19 pp.
30. Míguez, Joaquín; Crisan, Dan; Djurić, Petar M. On the convergence of two sequential Monte Carlo methods for maximum a posteriori sequence estimation and stochastic global optimization. Stat. Comput. 23 (2013), no. 1, 91–107.
31. Crisan, Dan; Delarue, François Sharp derivative bounds for solutions of degenerate semi-linear partial differential equations. J. Funct. Anal. 263 (2012), no. 10, 3024–3101.
32. Crisan, D.; Manolarakis, K. Solving backward stochastic differential equations using the cubature method: application to nonlinear pricing. SIAM J. Financial Math. 3 (2012), no. 1, 534–571.
33. Crisan, D.; Obanubi, O. Particle filters with random resampling times. Stochastic Process. Appl. 122 (2012), no. 4, 1332–1368.
34. Crisan, D., Manolarakis, K., Probabilistic methods for semilinear partial differential equations. Applications to finance, ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 44, No. 5 pp 1107–1133, 2010.
35. Crisan, D., Manolarakis, K., Touzi, N., On the Monte Carlo simulation of BSDEs: an improvement on the Malliavin weights. Stochastic Processes Appl. 120 , no. 7, 1133–1158, 2010.
36. Crisan, D., Xiong, J., Approximate McKean-Vlasov representations for a class of SPDEs, Stochastics 82 , no. 1-3, 53–68, 2010.
37. Crisan, D., Kouritzin, M. A., Xiong, J., Nonlinear filtering with signal dependent observation noise, Electronic Journal of Probability pp 1863-1883, 2009.
38. Crisan, D., Heine, K., Uniform Monte Carlo Approximation of Discrete Time Filter, Advances in Applied Probability, no 4 pp 979-1001, 2008 .
39. Crisan, D., Heine, K., “Stability of the discrete time filter in terms of the tails of noise distributions”, Journal of the London Mathematical Society, Vol. 78, No 2, pp 441-458, 2008.
40. Crisan, D., Xiong J., “A central limit type theorem for a class of particle filters”, Communications on Stochastic Analysis, No 1, pp 103-104, 2007.
41. Crisan, D., “Particle approximations for a class of stochastic partial differential equations”, Applied Mathematics and Optimization Journal, Vol 54, No 3, pp 293-317, 2006.
42. J.M.C. Clark, Crisan D., “On a robust version of the integral representation formula of nonlinear filtering”, Probability Theory and Related Fields, Vol 133, No 1 pp 43-56, 2005.
43. Crisan, D., “Superprocesses in random environments’’, Proceedings of The Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences. 460 no. 2041, pp 243—270, 2004.
44. Crisan, D., “Exact Rates of Convergence for a Branching Particle Approximation to the Solution of the Zakai Equation”, Annals of Probability, Vol. 31, No. 2, pp 693—718, 2003.
45. Crisan, D., Lyons. T., “Minimal Entropy Approximations and Optimal Algorithms for the Filtering Problem”, Monte Carlo Method and Applications, Vol 8, No 4, pp 343-357, 2002
46. Crisan, D., Doucet, A., “Convergence Results on Particle Filtering Methods for Practitioners”, IEEE Transactions on Signal Processing, Vol 50, No 3, pp 736-747, 2002.
47. Crisan, D., Del Moral, P., Lyons. T., “Interacting Particle Systems Approximations of the Kushner Stratonovitch Equation”, Advances in Applied Probability, vol.31, no. 3, pp 819-838, 1999.
48. Crisan, D., Del Moral, P., Lyons. T., “Discrete Filtering Using Branching and Interacting Particle Systems”, Markov Processes and Related Fields, Vol. 5, No. 3, 293-319, 1999.
49. Crisan, D., Lyons. T., “A Particle Approximation to the Solution of the Kushner-Stratonovitch Equation”, Probability Theory and Related Fields, Vol 115 no 4, 549-578, 1999.
50. Crisan, D., Gaines, J., Lyons. T., “Convergence of a Branching Particle Method to the Solution of the Zakai Equation”, SIAM Journal of Applied Probability, Vol 58 No. 5, 1568-1598, 1998.
51. Crisan, D., Lyons. T., “Non-Linear Filtering and Measure-Valued Processes”, Probability Theory and Related Fields, 109, 217-244, 1997.
52. Crisan, D., “Direct Computation of the Benes Filter Conditional Density”, Stochastics and Stochastic Reports, Vol 55, 47-54, 1995.
53. Crisan, D., ‘’Curvature Properties of a Special Class of Curves’’, Bull. Math. de la Soc. Sci. Math. de Roumanie, Tome 34 (82), no. 3, 219-222, 1990.