Rates for branching particle approximations of continuous-discrete filters

Annals of Applied Probability

Volumn 15, Issue 4, 2005, Pages 2739-2779

  Kouritzin, Michael A ^a   Sun, Wei ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b Gina Cody School of Engineering and Computer Science   (Canada)

Author keywords

Branching particle approximations; Filtering; Fourier analysis; Rates of convergence; Reference probability measure method

Indexed keywords

EID: 30844460779     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051605000000539     Document Type: Article

References (19)

1. BALLANTYNE, D. J., CHAN, H. Y. and KOURITZIN, M. A. (2000). A novel branching particle method for tracking. In Signal and Data Processing of Small Targets (O. E. Drummond, ed.) 277-287. SPIE, Bellingham, WA.
2. BLOUNT, D. and KOURITZIN, M. A. (2001). Holder continuity for spatial and path processes via spectral analysis. Probab. Theory Related Fields 119 589-603. MR1826409
3. CARTEA, Á. and HOWISON, S. (2004). Option pricing with Lévy-stable processes. Available at www.finance.ox.ac.uk/file_links/mf_papers/2004mf01.pdf.
4. CRISAN, D. (2003). Exact rates of convergence for a branching particle approximation to the solution of the Zakai equation. Ann. Probab. 31 693-718. MR1964946
5. CRISAN, D., DEL MORAL, P. and LYONS, T. J. (1999). Discrete filtering using branching and interacting particle systems. Markov Process. Related Fields 5 293-318. MR1710982
6. CRISAN, D. and LYONS, T. J. (1997). Nonlinear filtering and measure-valued processes. Probab. Theory Related Fields 109 217-244. MR1477650
7. DEL MORAL, P. (1996). Nonlinear filtering: Interacting particle resolution. Markov Process. Related Fields 2 555-579. MR1431187
8. DEL MORAL, P., KOURITZIN, M. A. and MICLO, L. (2001). On a class of discrete generation interacting particle systems. Electron. J. Probab. 6 1-26.
9. DEL MORAL, P. and MICLO, L. (2000). Branching and interacting particle systems approximations of Feynman-Kac Formulae with applications to nonlinear filtering. Séminaire de Probabilités XXXIV. Lecture Notes in Math. 1729 1-145. Springer, Berlin. MR1768060
10. GARROPPO, R. G., GIORDANO, S., PAGANO, M. and PROCISSI, G. (2002). Testing α-stable processes in capturing the queuing behavior of broadband teletraffic. Signal Processing 82 1861-1872.
11. KOURITZIN, M. A. (2000). Exact infinite dimensional filters and explicit solutions. In Stochastic Models (L. G. Gorostiza and B. G. Ivanoff, eds.) 265-282. Amer. Math. Soc., Providence, RI. MR1765015
12. KOURITZIN, M. A. and HEUNIS, A. J. (1994). A law of the iterated logarithm for stochastic processes defined by differential equations with a small parameter. Ann. Probab. 22 659-679. MR 1288126
13. LONGNECKER, M. and SERFLING, R. J. (1977). General moment and probability inequalities for the maximum partial sum. Acta Math. Acad. Sci. Hungar. 30 129-133. MR501261
14. MARINELLI, C. and RACHEV, S. T. (2002). Some applications of stable models in finance. Available at www.columbia.edu/~cm788/review.pdf.
15. MIKOSCH, T., RESNICK, S., ROOTZÉN, H. and STEGEMAN, A. (2002). Is network traffic approximated by stable Lévy motion or fractional Brownian motion? Ann. Appl. Probab. 1223-68. MR1890056
16. SAMORODNITSKY, G. and TAQQU, M. S. (1994). Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman and Hall, New York. MR1280932
17. SHERMAN, A. S. and PESKIN, C. S. (1986). A Monte Carlo method for scalar reaction diffusion equations. SIAM J. Sci. Statist. Comput. 7 1360-1372. MR857799
18. STEIN, E. (1970). Singular Integrals and Differentiability Properties of Functions. Princeton Univ. Press. MR290095
19. YOR, M. (1977). Sur les théories du filtrage et de la prédiction. Séminaire de Probabilités XI. Lecture Notes in Math. 581 257-297. Springer, Berlin. MR471060