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pro vyhledávání: '"Polunchenko, Aleksey S."'
We consider the classical Shiryaev--Roberts martingale diffusion, $(R_t)_{t\ge0}$, restricted to the interval $[0,A]$, where $A>0$ is a preset absorbing boundary. We take yet another look at the well-known phenomenon of quasi-stationarity (time-invar
Externí odkaz:
http://arxiv.org/abs/2310.19769
Autor:
Li, Kexuan, Polunchenko, Aleksey S.
For the classical Shiryaev--Roberts martingale diffusion considered on the interval $[0,A]$, where $A>0$ is a given absorbing boundary, it is shown that the rate of convergence of the diffusion's quasi-stationary cumulative distribution function (cdf
Externí odkaz:
http://arxiv.org/abs/1907.02676
We consider the quasi-stationary distribution of the classical Shiryaev diffusion restricted to the interval $[0,A]$ with absorption at a fixed $A>0$. We derive analytically a closed-form formula for the distribution's fractional moment of an {\em ar
Externí odkaz:
http://arxiv.org/abs/1904.02961
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 $A>0$.
Comment: 24 pages, 2 figures
Comment: 24 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/1805.07580
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 bou
Externí odkaz:
http://arxiv.org/abs/1711.05134
We consider the problem of quickest change-point detection where the observations form a first-order autoregressive (AR) process driven by temporally independent standard Gaussian noise. Subject to possible change are both the drift of the AR(1) proc
Externí odkaz:
http://arxiv.org/abs/1706.00824
Autor:
Polunchenko, Aleksey S.
We consider the first exit time of a Shiryaev-Roberts diffusion with constant positive drift from the interval $[0,A]$ where $A>0$. We show that the moment generating function (Laplace transform) of a suitably standardized version of the first exit t
Externí odkaz:
http://arxiv.org/abs/1702.08900
Autor:
Polunchenko, Aleksey S.
For the classical continuous-time quickest change-point detection problem it is shown that the randomized Shiryaev-Roberts-Pollak procedure is asymptotically nearly minimax-optimal (in the sense of Pollak 1985) in the class of randomized procedures w
Externí odkaz:
http://arxiv.org/abs/1607.03294
Autor:
Polunchenko, Aleksey S.
We offer a numerical study of the effect of headstarting on the performance of a Shiryaev-Roberts (SR) chart set up to control the mean of a normal process. The study is a natural extension of that previously carried out by Lucas and Crosier for the
Externí odkaz:
http://arxiv.org/abs/1607.00959
Autor:
Polunchenko, Aleksey S.
Publikováno v:
Sequential Analysis, Vol. 36, No. 1, pp. 126-149, March 2017
We consider the diffusion $(R_t^r)_{t\ge0}$ generated by the equation $dR_t^r=dt+\mu R_t^r dB_t$ with $R_0^r\triangleq r\ge0$ fixed, and where $\mu\neq0$ is given, and $(B_t)_{t\ge0}$ is standard Brownian motion. We assume that $(R_t^r)_{t\ge0}$ is s
Externí odkaz:
http://arxiv.org/abs/1606.06658