A homogenization approach to multiscale filtering

Procedia IUTAM

Volumn 5, Issue , 2012, Pages 34-45

  Imkeller, Peter ^a   Sri Namachchivaya, N ^b   Perkowski, Nicolas ^a   Yeong, Hoong C ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b United States of America   (United States)

Author keywords

Asymptotic expansion; BDSDE; Dimensional reduction; Homogenization; Nonlinear filtering; Particle filter; SPDE

Indexed keywords

ASYMPTOTIC ANALYSIS;

ASYMPTOTIC EXPANSION; BDSDE; DIMENSIONAL REDUCTION; HOMOGENIZATION; PARTICLE FILTER; SPDE;

NONLINEAR FILTERING;

EID: 84867461618     PISSN: None     EISSN: 22109838     Source Type: Conference Proceeding    
DOI: 10.1016/j.piutam.2012.06.005     Document Type: Conference Paper

References (21)

1. Lingala N, Namachchivaya N Sri, Perkowski N, Yeong HC. Particle filtering in high-dimensional chaotic systems. Submitted 2012.
2. Zakai M. On Optimal filtering of Diffusion Processes. Z. Wahrscheinlichkeitstheorie verw. Geb. 1969; 11(3): 230 -243.
3. Fujisaki M, Kallianpur G, Kunita H. Stochastic Differential Equations for the Non Linear Filtering Problem. Osaka J. Math. 1972; 9(1):19-40.
4. Bain A, Crisan D. Fundamentals of Stochastic Filtering. New York: Springer Verlag; 2009.
5. Kalliapur G. Stochastic Filtering Theory. New York: Springer-Verlag; 1980.
6. Liptser RS, Shiryaev N. Statistics of Random Processes: Applications. Springer; 2001.
7. Doucet A, de Freitas N, Gordon N. Sequential Monte Carlo Methods in Practice. New York: Springer Verlag; 2001.
8. Arulampalam MS, Maskell S, Gordon N, Clapp T.A Tutorial on particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking. IEEE Trans. Signal Process. 2002; 50(2): 174-188.
9. Snyder C, Bengtson T, Bickel P, Anderson J. Obstacles to high-dimensional particle filtering. Mon. Weather Rev. 2008: 136(12): 4629-4640.
10. Papanicolaou G, Stroock D, Varadhan SRS. Martingale Approach to Some Limit Theorems. Statistical Mehcanics and Dynamical Systems, and papers from 1976 Duke Turbulence Conference 1977; Duke University Mathematics Series.
11. Park J, Sowers R, Namachcivaya N Sri. Dimensional reduction in nonlinear filtering. Nonlinearity 2010: 23(2): 305-324.
12. Pardoux E. Stochastic partial differential equations and filtering of diffusion processes. Stochastics 1979; 3:127-167.
13. Pardoux E, Veretennikov AY. On Poisson equation and diffusion approximation 2. Ann. Probab. 2003; 31(3): 1166-1192.
14. Imkeller P, Namachchivaya N Sri, Perkowski N, Yeong HC. Dimensional reduction in nonlinear filtering: A homogenization approach. Submitted for publication 2012.
15. Bensoussan A, Blankenship GL. Nonlinear filtering with homogenization. Stochastics 1986; 17:67-90.
16. Ichihara N. Homogenization problem for stochastic partial differential equations of Zakai type. Stochastics Rep. 2004; 76(3): 243-266.
17. Pardoux E, Peng S. Backward Doubly Stochastic Differential Equations and Systems of Quasilinear SPDEs. Prob. Theory Related Fields 1994; 98: 209 -227.
18. Veretennikov AY. On Polynomial Mixing Bounds for Stochastic Differential Equations. Stochastic Process. Appl. 1997; 70(1): 115-127.
19. Karandikar RL. Interchanging the Order of Stochastic Integration and Ordinary Differentiation. Sankhya 1983; 45(1): 120- 124.
20. Park J, Namachchivaya N Sri, Yeong HC. Particle Filters in a Multiscale Environment: Homogenized Hybrid Particle Filter. J. Applied Mech. 2011; 78(6): 1-10.
21. Lorenz EN. Predictability: A problem partly solved. ECMWF Seminar Proceedings on Predictability 1995.