On Markovian sufficient statistics in non-additive disorder problems for jump-diffusion processes

make_name_string expected hash reference ORCID: 0000-0002-1346-2074 (2025) On Markovian sufficient statistics in non-additive disorder problems for jump-diffusion processes. In: Chigansky, P. and Kordzakhia, N., (eds.) Statistics of Random Processes and Optimal Control - A.N. Shiryaev’s Festschrift. UNSPECIFIED. (In Press)

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Abstract

We study the Bayesian problems of quickest (online) detection of unknown changes in the probabilistic characteristics of continuously observable jump-diffusion processes with the non-additive detection delay penalty criteria proposed by Shiryaev [49]. The reward functionals of the Bayesian risks are expressed through the current states of the multidimensional jump-diffusion processes playing the role of Markovian sufficient statistics in the appropriate optimal stopping problems. We derive stochastic differential equations for the components of the resulting multi-dimensional Markov processes and discuss possible extensions of the results to the case of observable discontinuous processes with stationary and independent increments forming natural exponential families.

Item Type:	Book Section
Additional Information:	© 2025
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics H Social Sciences > HA Statistics
Date Deposited:	27 Mar 2025 15:03
Last Modified:	27 Mar 2025 15:06
URI:	http://eprints.lse.ac.uk/id/eprint/127661

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