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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. T Cass, D Crisan, P Dobson, M Ottobre, Long-time behaviour of degenerate diffusions: UFG-type SDEs and time-inhomogeneous hypoelliptic processes, arXiv preprint arXiv:1805.01350, 2018.
2. C Cotter, D Crisan, DD Holm, W Pan, I Shevchenko, Modelling uncertainty using circulation-preserving stochastic transport noise in a 2-layer quasi-geostrophic model, arXiv preprint arXiv:1802.05711, 2018.
3. CJ Cotter, D Crisan, DD Holm, W Pan, I Shevchenko, Numerically modelling stochastic lie transport in fluid dynamics arXiv preprint arXiv:1801.09729, 2018.
4. D Crisan, F Flandoli, DD Holm, Solution properties of a 3D stochastic Euler fluid equation, arXiv preprint arXiv:1704.06989, 2017 (fast citation rate 26).
5. JF Chassagneux, D Crisan, F Delarue, A probabilistic approach to classical solutions of the master equation for large population equilibria, arXiv preprint arXiv:1411.3009.
6. D Crisan, S Ortiz-Latorre A high order time discretization of the solution of the non-linear filtering problem, arXiv preprint arXiv:1711.08012.
7. D Crisan, E McMurray, Cubature on Wiener Space for McKean-Vlasov SDEs with Smooth Scalar Interaction, arXiv preprint arXiv:1703.04177 .
8. JF Chassagneux, D Crisan, F Delarue, Numerical Method for FBSDEs of McKean-Vlasov Type arXiv preprint arXiv:1703.02007.
9. 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
10. J Barre, D Crisan, T Goudon, Two-dimensional pseudo-gravity model, arXiv preprint arXiv:1610.01296.
Published
11. D Crisan, PD Moral, J Houssineau, A Jasra, Unbiased multi-index Monte Carlo, Stochastic Analysis and Applications 36 (2), 257-273, 2018.
12. D Crisan, DD Holm, Wave breaking for the Stochastic Camassa–Holm equation, Physica D: Nonlinear Phenomena 376, 138-143, 2018.
13. D Crisan, E McMurray, Smoothing properties of McKean–Vlasov SDEs, Probability Theory and Related Fields 171 (1-2), 97-148, 2018.
14. D Crisan, J Míguez, G Ríos-Muñoz, On the performance of parallelisation schemes for particle filtering, EURASIP Journal on Advances in Signal Processing 2018 (1), 31, 2018.
15. D Crisan, J Miguez, Nested particle filters for online parameter estimation in discrete-time state-space Markov models, Bernoulli 24 (4A), 3039-3086, 2018. (fast citation rate 35).
16. D Crisan, C Janjigian, TG Kurtz, Particle representations for stochastic partial differential equations with boundary conditions Electronic Journal of Probability 23, 2018.
17. D Paulin, A Jasra, D Crisan, A Beskos, On concentration properties of partially observed chaotic systems, Advances in Applied Probability 50 (2), 440-479, 2018,
18. D Paulin, A Jasra, D Crisan, A Beskos, Optimization Based Methods for Partially Observed Chaotic Systems, Foundations of Computational Mathematics, 1-75, 2017,
19. 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.
20. D Crisan, E McMurray, Smoothing properties of McKean–Vlasov SDEs, Probability Theory and Related Fields, 1-52, 2017.
21. 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.
22. D Crisan, M Ottobre, Pointwise gradient bounds for degenerate semigroups (of UFG type) Proc. R. Soc. A 472, 2016.
23. 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.
24. Crisan, Dan; Otobe, Yoshiki; Peszat, Szymon Inverse problems for stochastic transport equations. Inverse Problems 31 (2015), no. 1, 015005, 20 pp.
25. 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.
26. 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.
27. Crisan, Dan; Míguez, Joaquín Particle-kernel estimation of the filter density in state-space models. Bernoulli 20 (2014), no. 4, 1879–1929.
28. 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.
29. Crisan, Dan; Xiong, Jie Numerical solution for a class of SPDEs over bounded domains. Stochastics 86 (2014), no. 3, 450–472.
30. 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.
31. 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.
32. Chassagneux, Jean-François; Crisan, Dan Runge-Kutta schemes for backward stochastic differential equations. Ann. Appl. Probab. 24 (2014), no. 2, 679–720.
33. Crisan, D.; Manolarakis, Konstantinos Second order discretization of backward SDEs and simulation with the cubature method. Ann. Appl. Probab. 24, 2014, no. 2, 652–678.
34. 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.
35. 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.
36. Míguez, Joaquín; Crisan, D.; 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.
37. Crisan, D.; Delarue, François Sharp derivative bounds for solutions of degenerate semi-linear partial differential equations. J. Funct. Anal. 263 (2012), no. 10, 3024–3101.
38. 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.
39. Crisan, D.; Obanubi, O. Particle filters with random resampling times. Stochastic Process. Appl. 122 (2012), no. 4, 1332–1368.
40. 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.
41. 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.
42. Crisan, D., Xiong, J., Approximate McKean-Vlasov representations for a class of SPDEs, Stochastics 82 , no. 1-3, 53–68, 2010.
43. Crisan, D., Kouritzin, M. A., Xiong, J., Nonlinear filtering with signal dependent observation noise, Electronic Journal of Probability pp 1863-1883, 2009.
44. Crisan, D., Heine, K., Uniform Monte Carlo Approximation of Discrete Time Filter, Advances in Applied Probability, no 4 pp 979-1001, 2008 .
45. 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.
46. 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.
47. 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.
48. 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.
49. 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.
50. 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.
51. 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
52. 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.
53. 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.
54. 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.
55. 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.
56. 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.
57. Crisan, D., Lyons. T., “Non-Linear Filtering and Measure-Valued Processes”, Probability Theory and Related Fields, 109, 217-244, 1997.
58. Crisan, D., “Direct Computation of the Benes Filter Conditional Density”, Stochastics and Stochastic Reports, Vol 55, 47-54, 1995.
59. 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.
Contributions to Books (refereed)
60. Crisan, D.; Manolarakis, K.; Nee, C. Cubature methods and applications. Paris-Princeton Lectures on Mathematical Finance 2013, 203–316, Lecture Notes in Math., 2081, Springer, Cham, 2013.
61. Crisan, D. Discretizing the continuous-time filtering problem: order of convergence. The Oxford handbook of nonlinear filtering, 572–597, Oxford Univ. Press, Oxford, 2011.
62. Crisan D., Ghazali S., “On the convergence rates of a general class of weak approximations”, Stochastic Differential Equations – Theory and Applications, Eds. P. Baxendale, S. Lototsky, World Scientific, 2007.
63. Crisan, D., “Particle Filters. A Theoretical Perspective”, Chapter 2 in “Sequential Monte Carlo Methods in Practice”, Eds. A. Doucet, J. F. G. de Freitas, N. J. Gordon, pp 17-43, Springer Verlag, 2001.
Published Conference Proceedings (refereed)
64. J Míguez, D Crisan, IP Marino, Particle filtering for Bayesian parameter estimation in a high dimensional state space model, Signal Processing Conference (EUSIPCO), 2015 23rd European, 1241-1245.
65. Crisan D, Li K, 2011, GENERALISED PARTICLE FILTERS WITH GAUSSIAN MEASURES, 19TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO-2011), Pages: 659-663, ISSN: 2076-1465.
66. Crisan, D.; Manolarakis, K. Solving backward stochastic differential equations using the cubature method. Application to nonlinear pricing. Progress in analysis and its applications, 389–397, World Sci. Publ., Hackensack, NJ, 2010.
67. Crisan, D. Xiong, J., “An approximate McKean-Vlasov model for the stochastic filtering problem” Conference Oxford sur les méthodes de Monte Carlo séquentielles, ESAIM Proc., 19, EDP Sci., Les Ulis, pp 18-21, 2007.
68. Crisan, D. Xiong, J., “Numerical solutions for a class of SPDEs over bounded domains” Conference Oxford sur les méthodes de Monte Carlo séquentielles, ESAIM Proc., 19, EDP Sci., Les Ulis, pp 121-125, 2007.
69. Crisan, D., “Particle Filters in a Continuous Time Framework”, Proceedings of the Nonlinear Statistical Signal Processing Workshop 13-15 September 2006 IEEE, pp 73-78, 2006.
70. Crisan, D., “Numerical Methods for Solving the Stochastic Filtering Problem”, Numerical methods and stochastics (Toronto, ON, 1999), pp 1-20, Fields Inst. Commun., Vol. 34, Amer. Math. Soc., Providence, RI, 2002.
71. Crisan, D., Lyons. T., “Optimal Filtering on Discrete Sets”, in “Numerical methods and stochastics”, Numerical methods and stochastics (Toronto, ON, 1999), pp 21-27, Fields Inst. Commun., Vol. 34, Amer. Math. Soc., Providence, RI, 2002.
Other Papers
72. Dan Crisan and Kai Li, A central limit type theorem for Gaussian mixture approximations to the nonlinear filtering problem, Preprint.
73. Crisan, D., Doucet, A., “Convergence of Sequential Monte Carlo Methods” Technical Report Cambridge University, CUED/FINFENG /TR381, 2000.
74. Crisan, D., Grunwald, M., “Comparison of Branching Algorithms versus Resampling Algorithms”, Statistical Laboratory Research Report 1999-9, 1999.