A particle approximation of the solution of the Kushner-Stratonovitch equation

Probability Theory and Related Fields

Volumn 115, Issue 4, 1999, Pages 549-578

  Crisan, D ^a   Lyons, T ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033261066     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050249     Document Type: Article

References (20)

1. Aldous, D.: Slopping Times and Tightness, Ann. Prob., 6 (1978)
2. Bensoussan, A.: Stochastic Control of Partially Observable Systems, Cambridge University Press, Cambridge (1992)
3. Bensoussan, A., Glowinski, R., Rascanu A.: Approximation of the Zakai equation by splitting up method SIAM Journal on Control and Optimization, Vol. 28, No 6, pp. 1420-1431 (1990)
4. Bensoussan, A., Glowinski, R., Rascanu A.: Approximation of some stochastic differential equations by the splitting up method, Applied Mathematics and Optimization, Vol. 25, No 1, pp. 81-106 (1992)
5. Carpenter, J. R., Clifford, P., Fearnhead, P.: Sampling strategies for Monte Carlo filters for non-linear systems, IEE Colloquium Digest 243, 6/1-6/3 (1996)
6. Crisan, D., Lyons,T.: Nonlinear Filtering and Measure Valued Processes, Probability Theory and Related Fields 109, pp. 217-244 (1997)
7. Crisan, D., Gaines, J., Lyons, T.: Convergence of a Branching Particle Method to the Solution of the Zakai Equation, to appear in SIAM Journal of Applied Mathematics (1998)
8. Crisan, D., Grunvald M.: Comparison of Branching Algorithms versus Resampling Algorithms, submitted to the Annals of Applied Probability.
9. Crisan,D.: Uniform Upper Bounds for the Solution of the Zakai Equation, Preprint.
10. Del Moral, P.: Non Linear Filtering using Random Particles. Theory of Probability and its Applications, Vol. 40, (4), pp. 690-701 (1996)
11. Del Moral, P.: Non-linear Filtering: Interacting particle solution. Markov Processes and Related Fields, Vol. 2, pp. 555-580 (1996)
12. Enachescu, D.M.: Monte Carlo Method for Nonlinear Filtering. Proceedings of the 4th Pannonian Symposium on Mathematical Statistics, Mathematical Statistics and Applications. Klüver (1985)
13. Florchingen, P., Le Gland, F: Time discretization of the Zakai equation for diffusion processes observed in correlated noise, Stochastics and Stochastics Reports volume 35, numero 4, pp. 233-256 (1991)
14. Le Gland, F.: Splitting-up Approximation for the SPDE's and SDE's with Application to Nonlinear Filtering, Stochastic Partial Differential Equations and their Applications, Lecture Notes in Control and Information Sciences, Vol. 176 (1992)
15. Gordon, N. J., Salmon, D. J., Smith, A. F. M.: Novel Approach to non-linear/non-Gaussian Bayesian state estimation., IEE Proceedings, Part F, Vol. 140, (2), 107-113 (1993)
16. Kurtz, T. G., Ocone, D. L.: Unique Characterization of Conditional Distribution in Nonlinear Filtering. The Annals of Probability, Vol. 16, No. 1, 80-107 (1988)
17. Kushner, H. J.: Probability methods for approximations in stochastic control and for elliptic equations, New York: Academic Press, (Mathematics in science and engineering; Vol. 129) (1977)
18. Liptser, R. S., Shiryayev A. N.: The Statistics of Random Processes I. General Theory., Springer-Verlag, (1977)
19. Pardoux, E.: Filtrage Non Linéaire et Equations aux Dérivées Partielles Stochastiques Associées, Ecole d'Eté de Probabilités de Saint-Flour XIX - 1989, Lecture Notes in Mathematics, 1464, Springer-Verlag (1991)
20. Roelly-Coppoletta, S.: A Criterion of Convergence of Measure-Valued Processes: Application to Measure Valued Branching Processes, Stochastics, 1986, Vol 17, pp. 43-65