Geodesic
A note on the quasi-stationary distribution of the Shiryaev martingale on the positive half-line
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 565-583

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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 $[A,+\infty)$ 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 [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.
Keywords: quasi-stationary distribution, Whittaker function.
Mots-clés : martingale Shiryaev diffusion process 
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     author = {A. S. Polunchenko and S. Mart{\'\i}nez and J. San Mart{\'\i}n},
     title = {A note on the quasi-stationary distribution of the {Shiryaev} martingale on the positive half-line},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {565--583},
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     volume = {63},
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A. S. Polunchenko; S. Martínez; J. San Martín. A note on the quasi-stationary distribution of the Shiryaev martingale on the positive half-line. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 3, pp. 565-583. http://geodesic.mathdoc.fr/item/TVP_2018_63_3_a8/