Abstract
In this paper we consider a problem of filtering for a stochastic dynamical system (X t , t ≥ 0) from observations (θ t , t ≥ 0) of the form where h(t, x) is some non-anticipating function and Y t is an annealing noice that is a Lévy process. This problem arises from Simulated Annealing Theory applied to Filtering. The paper is organized as follows. In section 2, we give the dynamics for the system in emphasizing on Lévy process. Section 3 stands for annealing process that is the solution of a diffusion equation and in Section 4, after introducing the concept of Lévy annealing noice we established a differential equation for the filter π t (f) of the considered dynamical system
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References
B. Grigelionis, On Non-linear Filtering theory and Absolute Continuity of Measure corresponding to Stochastic Processes. Lecture Notes in Math. 330, Proc. USSR Japan Symp. on Prob, Springer Berlin, (1973), 80-94.
Tran Hung Thao, Optimal State Estimation for A Stochastic Dynamical System from Point Process Observation. Sonderdruck aus Methods of Operations Research. Ulm, 62(1989), 421–430.
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© 1997 Springer Science+Business Media Dordrecht
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Thao, T.H. (1997). A Differential Equation for Filtering of a Stochastic Dynamical System. In: van Groesen, E., Soewono, E. (eds) Differential Equations Theory, Numerics and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5157-3_23
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DOI: https://doi.org/10.1007/978-94-011-5157-3_23
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6168-1
Online ISBN: 978-94-011-5157-3
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