A note on the quasi-stationary distribution of the shiryaev martingale on the positive half-line
Author
dc.contributor.author
Polunchenko, A. S.
Author
dc.contributor.author
Martínez, S.
Author
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Martín, J. San
Admission date
dc.date.accessioned
2019-10-30T15:18:50Z
Available date
dc.date.available
2019-10-30T15:18:50Z
Publication date
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2019
Cita de ítem
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Theory of Probability and its Applications, Volumen 63, Issue 3, 2019, Pages 464-478
Identifier
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10957219
Identifier
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0040585X
Identifier
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10.1137/S0040585X97T989179
Identifier
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https://repositorio.uchile.cl/handle/2250/172117
Abstract
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We obtain a closed-form formula for the quasi-stationary distribution of the classical Shiryaev martingale diffusion considered on the positive half-line [A, +∞) withA>0 fixed; the state space’s left endpoint is assumed to be the killing boundary. The formula is obtained analytically as the solution of the appropriate singular Sturm–Liouville problem; the latter was first considered in section 7.8.2 of [P. Collet, S. Martínez, and J. San Martín, Quasi-Stationary Distributions. Markov Chains, Diffusions and Dynamical Systems, Springer, Heidelberg, 2013] but has heretofore remained unsolved.
Lenguage
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en
Publisher
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Society for Industrial and Applied Mathematics Publications