Proximal Recursion for the Wonham Filter

D.W. Stroock, An introduction to Markov processes . Springer Science & Business Media, vol. 230, 2 nd ed.; 2013

Original

1909

Earlier work this paper cites.

W.M. Wonham, “Some applications of stochastic differential equations to optimal nonlinear filtering”. Journal of the Society for Industrial and Applied Mathematics, Series A: Control , Vol. 2, No. 3, pp. 347–369, 1964

1964

Earlier work this paper cites.

K. Yosida, Functional Analysis , Spinger-Verlag, 1964

1964

Earlier work this paper cites.

J-J. Moreau, “Proximité et dualité dans un espace hilbertien”. Bulletin de la Société mathématique de France , Vol. 93, pp. 273–299, 1965

1965

Earlier work this paper cites.

R.T. Rockafeller, “Monotone operators and the proximal point algorithm”. SIAM Journal on Control and Optimization , Vol. 14, No. 5, pp. 877–898, 1976

1976

Earlier work this paper cites.

M. Teboulle, “Entropic proximal mappings with applications to nonlinear programming”. Mathematics of Operations Research , Vol. 17, No. 3, pp. 670–690, 1992

1992

Earlier work this paper cites.

Y. Censor, and S.A. Zenios, “Proximal minimization algorithm with D-functions”. Journal of Optimization Theory and Applications , Vol. 73, No. 3, pp. 451–464, 1992

1992

Earlier work this paper cites.

R. Jordan, D. Kinderlehrer, and F. Otto, “The variational formulation of the Fokker–Planck equation”. SIAM Journal on Mathematical Analysis , Vol. 29, No. 1, pp. 1–17, 1998

1998

Cited alongside, same era.

Q. Zhang, Y.G. George, and J.B. Moore, “Two-time-scale approximation for Wonham filters”. IEEE Transactions on Information Theory , Vol. 53, No. 5, pp. 1706–1715, 2007

2007

Cited alongside, same era.

L. Ambrosio, N. Gigli, and G. Savaré, Gradient flows: in metric spaces and in the space of probability measures . Springer Science & Business Media, 2008

2008

Cited alongside, same era.

H.H. Bauschke, and P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces . CMS Books in Mathematics, Springer; 2011

2011

Cited alongside, same era.

N. Parikh, and S. Boyd, “Proximal algorithms”. Foundations and Trends ® in Optimization , Vol. 1, No. 3, pp. 127–239, 2014

T. Yang, P.G. Mehta, and S.P. Meyn, “Feedback particle filter for a continuous-time Markov chain”. IEEE Transactions on Automatic Control , Vol. 61, No. 2, pp. 556–561, 2016

2016

Later among the works it cites.

A. Halder, and T.T. Georgiou, “Gradient flows in uncertainty propagation and filtering of linear Gaussian systems”. 2017 IEEE 56th Annual Conference on Decision and Control (CDC) , pp. 3081–3088, 2017

2017

Later among the works it cites.

——, “Gradient flows in filtering and Fisher-Rao geometry”. 2018 Annual American Control Conference (ACC) , pp. 4281–4286, 2018

2018

Later among the works it cites.

C. Zhang, A. Taghvaei, and P.G. Mehta, “A mean-field optimal control formulation for global optimization”. IEEE Transactions on Automatic Control , Vol. 64, No. 1, pp. 282–289, 2018

2018

Later among the works it cites.

K.F. Caluya, and A. Halder, “Proximal recursion for solving the Fokker-Planck equation”. 2019 Annual American Control Conference (ACC) , accepted, preprint arXiv:1809.10844, 2019. web: https://arxiv.org/pdf/1809.10844.pdf