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This article is cited in 5 scientific papers (total in 5 papers)
A note on the quasi-stationary distribution of the Shiryaev martingale on the positive half-line
A. S. Polunchenkoa, S. Martínezb, J. San Martínb a Department of Mathematical Sciences, State University of New York at Binghamton, Binghamton, NY, USA
b Departamento de Ingeniería Matemática and Centro de Modelamiento Matemático, UMI-CNRS 2807, Universidad de Chile, Santiago, Chile
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
[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, martingale Shiryaev diffusion process, Whittaker function.
Received: 20.10.2017 Accepted: 30.10.2017
Citation:
A. S. Polunchenko, S. Martínez, J. San Martín, “A note on the quasi-stationary distribution of the Shiryaev martingale on the positive half-line”, Teor. Veroyatnost. i Primenen., 63:3 (2018), 565–583; Theory Probab. Appl., 63:3 (2019), 464–478
Linking options:
https://www.mathnet.ru/eng/tvp5154https://doi.org/10.4213/tvp5154 https://www.mathnet.ru/eng/tvp/v63/i3/p565
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