Gapeev, Pavel V. (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: | 21 Sep 2025 00:15 |
| URI: | http://eprintstest.lse.ac.uk/id/eprint/127661 |
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