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Nonlinear filtering for Markov systems with delayed observations

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This paper deals with nonlinear filtering problems with delays, i.e., we consider a system (X,Y), which can be represented by means of a system (X,Ŷ), in the sense that Yt = Ŷa(t), where a(t) is a delayed time transformation. We start with X being a Markov process, and then study Markovian systems, not necessarily diffusive, with correlated noises. The interest is focused on the existence of explicit representations of the corresponding filters as functionals depending on the observed trajectory. Various assumptions on the function a(t) are considered.








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  • Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica 1, I 00133 Roma, Italy
  • Département de Mathématiques, Université de Metz, 23 Allée des Oeillets, F 57160 Moulins les Metz, France
  • Dipartimento di Matematica, Università di Roma “La Sapienza”, piazzale A. Moro 2, I 00185 Roma, Italy


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