Abstract
We derive analytic closed-form moment and Laplace transform formulae for the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval [0, A] with absorption at a given \(A>0\).
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Acknowledgements
The authors would like to thank the two anonymous referees for the careful reading of the manuscript and pertinent comments; the referees’ constructive feedback helped substantially improve the quality of this work and shape its final form.
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The effort of A.S. Polunchenko was partially supported by the Simons Foundation via a Collaboration Grant in Mathematics under Award # 304574. The work of A. Pepelyshev was partially supported by the Russian Foundation for Basic Research under Projects ## 17-01-00267-a and 17-01-00161-a.
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Polunchenko, A.S., Pepelyshev, A. Analytic moment and Laplace transform formulae for the quasi-stationary distribution of the Shiryaev diffusion on an interval. Stat Papers 59, 1351–1377 (2018). https://doi.org/10.1007/s00362-018-1019-8
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DOI: https://doi.org/10.1007/s00362-018-1019-8
Keywords
- Laplace transform
- Markov diffusions
- Quasi-stationarity
- Shiryaev process
- Special functions
- Stochastic processes