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Convergence in probability

Maurice Frechet
- Vol. 8, Iss: 4, pp 3-50
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The article was published on 1930-03-15 and is currently open access. It has received 48 citations till now. The article focuses on the topics: Convergence of random variables.

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Long-Term Memory in Stock Market Prices

TL;DR: In this paper, a test for long-run memory that is robust to short-range dependence is developed, which is a simple extension of Mandelbrot's "range over standard deviation" or R/S statistic, for which the relevant asymptotic sampling theory is derived via functional central limit theory.
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Constrained Markov Decision Processes

Eitan Altman
TL;DR: In this paper, a unified approach for the study of constrained Markov decision processes with a countable state space and unbounded costs is presented, where a single controller has several objectives; it is desirable to design a controller that minimize one of cost objectives, subject to inequality constraints on other cost objectives.
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Detection of intensity change points in time-resolved single-molecule measurements.

TL;DR: This new method uses a generalized likelihood ratio test that determines the location of an intensity change point based on individual photon arrival times and is applied recursively to an entire single molecule intensity trajectory, thus finding each change points.
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Nonparametric estimation in a nonlinear cointegration type model

TL;DR: In this article, the authors derived an asymptotic theory of nonparametric estimation for a time series regression model, where the class of nonstationary processes allowed for this model is a subclass of the classes of null recurrent Markov chains.
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Information Bounds and Optimal Analysis of Dynamic Single Molecule Measurements

TL;DR: A general approach to the estimation of molecular parameters based on individual photon arrival times is presented, and it is shown that this algorithm reaches the theoretical limit, extracting the maximal information out of the data.