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Winning rate in the full information bestchoice problem, available at arXiv
, 2005
"... Following a longstanding suggestion by Gilbert and Mosteller, we derive an explicit formula for the asymptotic winning rate in the fullinformation problem of the best choice. ..."
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Following a longstanding suggestion by Gilbert and Mosteller, we derive an explicit formula for the asymptotic winning rate in the fullinformation problem of the best choice.
Recognising the Last Record of a Sequence
, 2006
"... We study the bestchoice problem for processes which generalise the process of records from Poissonpaced i.i.d. observations. Under the assumption that the observer knows distribution of the process and the horizon, we determine the optimal stopping policy and for a parametric family of problems al ..."
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We study the bestchoice problem for processes which generalise the process of records from Poissonpaced i.i.d. observations. Under the assumption that the observer knows distribution of the process and the horizon, we determine the optimal stopping policy and for a parametric family of problems also derive an explicit formula for the maximum probability of recognising the last record. 1
Optimal Stopping with RankDependent Loss
, 705
"... For τ a stopping rule adapted to a sequence of n iid observations, we define the loss to be E[q(Rτ)], where Rj is the rank of the jth observation, and q is a nondecreasing function of the rank. This setting covers both the best choice problem with q(r) = 1(r> 1), and Robbins’ problem with q(r) ..."
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For τ a stopping rule adapted to a sequence of n iid observations, we define the loss to be E[q(Rτ)], where Rj is the rank of the jth observation, and q is a nondecreasing function of the rank. This setting covers both the best choice problem with q(r) = 1(r> 1), and Robbins’ problem with q(r) = r. As n → ∞ the stopping problem acquires a limiting form which is associated with the planar Poisson process. Inspecting the limit we establish bounds on the stopping value and reveal qualitative features of the optimal rule. In particular, we show that the complete history dependence persists in the limit, thus answering a question asked by Bruss [3] in the context of Robbins ’ problem.
Elect. Comm. in Probab. 13 (2008), 187–193 ELECTRONIC COMMUNICATIONS in PROBABILITY CORNERS AND RECORDS OF THE POISSON PRO CESS IN QUADRANT
, 2007
"... The scaleinvariant spacings lemma due to Arratia, Barbour and Tavare ́ establishes the distributional identity of a selfsimilar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of a certain set of extreme points of the ..."
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The scaleinvariant spacings lemma due to Arratia, Barbour and Tavare ́ establishes the distributional identity of a selfsimilar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of a certain set of extreme points of the unit Poisson process in the positive quadrant. 1
Corners and Records of the Poisson Process in Quadrant
, 709
"... The scaleinvariant spacings lemma due to Arratia, Barbour and Tavaré establishes the distributional identity of a selfsimilar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of a certain set of extreme points of the un ..."
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The scaleinvariant spacings lemma due to Arratia, Barbour and Tavaré establishes the distributional identity of a selfsimilar Poisson process and the set of spacings between the points of this process. In this note we connect this result with properties of a certain set of extreme points of the unit Poisson process in the positive quadrant.