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arXiv · 1711.05134

A Note on the Quasi-Stationary Distribution of the Shiryaev Martingale on the Positive Half-Line

Aleksey S. Polunchenko·Servet Martinez·Jaime San Martin
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Abstract

We obtain a closed-form formula for the quasi-stationary distribution of the classical Shiryaev martingale diffusion considered on the positive half-line $[A,+\infty)$ with $A>0$ 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 Collet et al. (2013), but has heretofore remained unsolved.

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Aleksey S. Polunchenko, Servet Martinez, Jaime San Martin. 2017-11-14. A Note on the Quasi-Stationary Distribution of the Shiryaev Martingale on the Positive Half-Line. https://arxiv.org/abs/1711.05134

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