Uniqueness of the filtering equations in the space of measures | Vidéo | Carmin.tv

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Uniqueness of the filtering equations in the space of measures

By Etienne Pardoux

Appears in collection : Probability/PDE Interactions: Interface Models and Particle Systems / Interactions EDP/Probabilités : interfaces et systèmes de particules

We consider a general class of filtering equations, where all coefficients depend upon the observation process, and the signal and observation noises are correlated. We prove uniqueness of the measure valued solution of the Zakai equation via a duality argument with a backward stochastic partial differential equation. This is joint work with Dan Crisan, Imperial College, London.

Information about the video

Date of recording 28/04/2022
Date of publication 10/05/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19909803
Cite this video Pardoux, Etienne (28/04/2022). Uniqueness of the filtering equations in the space of measures. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19909803
URL https://dx.doi.org/10.24350/CIRM.V.19909803

Domain(s)

Probability

Bibliography

BAIN, Alan et CRISAN, Dan. Fundamentals of stochastic filtering. New York : Springer, 2009. - https://doi.org/10.1007/978-0-387-76896-0
BENSOUSSAN, Alain. Stochastic control of partially observable systems. Cambridge University Press, 1992. - https://doi.org/10.1017/CBO9780511526503
DU, Kai et MENG, Qingxin. A revisit to W2n-theory of super-parabolic backward stochastic partial differential equations in Rd. Stochastic Processes and their Applications, 2010, vol. 120, no 10, p. 1996-2015. - http://dx.doi.org/10.1016/j.spa.2010.06.001
DU, Kai, TANG, Shanjian, et ZHANG, Qi. Wm, p-solution (p⩾ 2) of linear degenerate backward stochastic partial differential equations in the whole space. Journal of Differential Equations, 2013, vol. 254, no 7, p. 2877-2904. - https://doi.org/10.1016/j.jde.2013.01.013
PARDOUX, Etienne et PENG, Shige. Adapted solution of a backward stochastic differential equation. Systems & Control Letters, 1990, vol. 14, no 1, p. 55-61. - https://doi.org/10.1016/0167-6911(90)90082-6

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