<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">This paper deals with nonlinear filtering problems with delays, i. e., we consider a system (<bold><italic>X, Y</italic></bold>), which can be represented by means of a system (<bold><italic>X, Ŷ</italic></bold>), in the sense that <italic>Yt = Ŷa(t)</italic>, where <italic>a(t)</italic> is a delayed time transformation. We start with <bold><italic>X</italic></bold> 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 <italic>a(t)</italic> are considered.</abstract>

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.

Nonlinear Filtering for Markov Systems with Delayed Observations

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

International Journal of Applied Mathematics and Computer Science

{"article-title":"Nonlinear Filtering for Markov Systems with Delayed Observations"}

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...

Nonlinear Filtering for Markov Systems with Delayed Observations

Pubblicato online: 02 apr 2009

Pagine: 49 - 58

DOI: https://doi.org/10.2478/v10006-009-0004-8

Parole chiave
nonlinear filtering, jump processes, diffusion processes, Markov processes, stochastic delay differential equation

This content is open access.

Nonlinear Filtering for Markov Systems with Delayed Observations

Pubblicato online: 02 apr 2009

Pagine: 49 - 58

DOI: https://doi.org/10.2478/v10006-009-0004-8

Parole chiavenonlinear filtering, jump processes, diffusion processes, Markov processes, stochastic delay differential equation

This content is open access.

Parole chiave
nonlinear filtering, jump processes, diffusion processes, Markov processes, stochastic delay differential equation