An approximation for the Zakai equation

Applied Mathematics and Optimization

Volumn 45, Issue 1, 2002, Pages 23-44

  Hu, Y ^a   Kallianpur, G ^b   Xiong, J ^c  

^a UNIVERSITY OF KANSAS   (United States)

^b University of North Carolina at Chapel Hill   (United States)

^c UNIVERSITY OF TENNESSEE   (United States)

Author keywords

Filtering; Stochastic differential equation; Weak convergence; Zakai equation

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FILTRATION; PARTIAL DIFFERENTIAL EQUATIONS; TOPOLOGY;

POLYGONAL APPROXIMATION; STOCHASTIC DIFFERENTIAL EQUATION; WEAK CONVERGENCE; ZAKAI EQUATION;

APPROXIMATION THEORY;

EID: 1542371866     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00245-001-0024-8     Document Type: Article

References (12)

1. A. Bhatt, G. Kallianpur and R. Karandikar, Uniqueness and robustness of solution of measure valued equations of nonlinear filtering, Ann. Probab., 23 (1995), 1895-1938.
2. A. Bhatt and R. Karandikar, Invariant measures and evolution equations for Markov processes characterized via martingale problems, Ann. Probab., 21 (1993), 2246-2268.
3. A. Budhiraja and G. Kallianpur, Approximations to the solution of the Zakai equation using multiple Wiener and Stratonovitch integral expansions, Stochastics Stochastics Rep., 56 (1996), 271-315.
4. M. Chaleyat-Maurel and D. Michel, A Stroock Varadhan support theorem in non-linear filtering theory. Probab. Theory Related Fields, 84 (1990), 119-139.
5. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, 1964.
6. S.W. He, J. G. Wang and J. A. Yan, Semimartingale and Stochastic Analysis (in Chinese), Science Press, Beijing, 1995.
7. N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusions, North-Holland, Amsterdam, 1989.
8. H. Kunita, Stochastic partial differential equations connected with nonlinear filtering, in Nonlinear Filtering and Stochastic Control, ed. by S. K. Mitter and A. Moro, Lecture Notes in Mathematics 972, Springer-Verlag, Berlin, 1982, pp. 100-169.
9. M. Métivier, Semimartingales, de Gruyter, New York, 1982.
10. J. M. Moulinier, Théorèemes limites pour des processus à un ou deux paramètres. Thèse de 3ème cycle, Université de Paris VI, 1982.
11. J. M. Moulinier, Théorèmes limites pour les équations différentielles stochastiques. Bull. Sci. Math. (2) 112(1988), 118-210.
12. E. Wong and M. Zakai, On the relation between ordinary and stochastic differential equations, Internat. J. Engrg. Sci., 3 (1965), 213-229.