Stochastic filtering of a pure jump process with predictable jumps and path-dependent local characteristics

Elena Bandini, Alessandro Calvia and Katia Colaneri

Stochastic Processes and their Applications, 2022, vol. 151, issue C, 396-435

Abstract: The objective of this paper is to study the filtering problem for a system of partially observable processes (X, Y), where X is a non-Markovian pure jump process representing the signal and Y is a general jump diffusion which provides observations. Our model covers the case where both processes are not necessarily quasi left-continuous, allowing them to jump at predictable stopping times. By introducing the Markovian version of the signal, we are able to compute an explicit equation for the filter via the innovations approach.

Keywords: Stochastic filtering; Pure jump process; Jump–diffusion process; Non quasi-left-continuous random measure; Path-dependent local characteristics (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.06.007

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