We deal with the filtering problem of a general jump diffusion process, X, when the observation process, Y, is a correlated jump diffusion process having common jump times with X. In this setting, at any time t the σ-algebra F^Y_t provides all the available information about X_t , and the central goal is to characterize the filter, π_t , which is the conditional distribution of X_t given observations F^Y_t. To this end, we prove that π t solves the Kushner-Stratonovich equation and, by applying the filtered martingale problem approach (see Kurtz and Ocone (1988)), that it is the unique weak solution to this equation. Under an additional hypothesis, we also provide a pathwise uniqueness result.

Ceci, C., Colaneri, K. (2012). Nonlinear filtering for jump diffusion observations. ADVANCES IN APPLIED PROBABILITY, 44(3), 678-701 [10.1239/aap/1346955260].

Nonlinear filtering for jump diffusion observations

Colaneri K.
2012-01-01

Abstract

We deal with the filtering problem of a general jump diffusion process, X, when the observation process, Y, is a correlated jump diffusion process having common jump times with X. In this setting, at any time t the σ-algebra F^Y_t provides all the available information about X_t , and the central goal is to characterize the filter, π_t , which is the conditional distribution of X_t given observations F^Y_t. To this end, we prove that π t solves the Kushner-Stratonovich equation and, by applying the filtered martingale problem approach (see Kurtz and Ocone (1988)), that it is the unique weak solution to this equation. Under an additional hypothesis, we also provide a pathwise uniqueness result.
2012
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
Settore SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE
English
Con Impact Factor ISI
Filtering; jump diffusion process
Ceci, C., Colaneri, K. (2012). Nonlinear filtering for jump diffusion observations. ADVANCES IN APPLIED PROBABILITY, 44(3), 678-701 [10.1239/aap/1346955260].
Ceci, C; Colaneri, K
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/218959
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