scholarly journals Convergence of moments of twisted COE matrices

2021 ◽  
Vol 62 (6) ◽  
pp. 063502
Author(s):  
Gregory Berkolaiko ◽  
Laura Booton
Keyword(s):  
Convergence Of Moments

Marked point processes as limits of Markovian arrival streams

1993 ◽  
Vol 30 (02) ◽  
pp. 365-372 ◽  
Author(s):  
Søren Asmussen ◽  
Ger Koole
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Marked Point ◽  
The State ◽  
Marked Point Processes ◽  
Marked Point Process ◽  
State Transitions ◽  
Poisson Arrival ◽  
Convergence Of Moments ◽  
Environmental Process

A Markovian arrival stream is a marked point process generated by the state transitions of a given Markovian environmental process and Poisson arrival rates depending on the environment. It is shown that to a given marked point process there is a sequence of such Markovian arrival streams with the property that as m →∞. Various related corollaries (involving stationarity, convergence of moments and ergodicity) and counterexamples are discussed as well.

The existence of moments for stationary Markov chains

1983 ◽  
Vol 20 (01) ◽  
pp. 191-196 ◽  
Author(s):  
R. L. Tweedie
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Time Dependent ◽  
General Function ◽  
Convergence Of Moments ◽  
Special Cases

We give conditions under which the stationary distribution π of a Markov chain admits moments of the general form ∫ f(x)π(dx), where f is a general function; specific examples include f(x) = xr and f(x) = esx . In general the time-dependent moments of the chain then converge to the stationary moments. We show that in special cases this convergence of moments occurs at a geometric rate. The results are applied to random walk on [0, ∞).

scholarly journals Statistical Aspects of Wasserstein Distances

2019 ◽  
Vol 6 (1) ◽  
pp. 405-431 ◽  
Author(s):  
Victor M. Panaretos ◽  
Yoav Zemel
Keyword(s):  
Probability Distributions ◽  
The Other ◽  
Mass Transportation ◽  
Complex Objects ◽  
Convergence Of Moments ◽  
Natural Notion ◽  
Versatile Tool ◽  
Probability Mass ◽  
Minimal Effort ◽  
Wasserstein Distances

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in order to recover the other distribution. They are ubiquitous in mathematics, with a long history that has seen them catalyze core developments in analysis, optimization, and probability. Beyond their intrinsic mathematical richness, they possess attractive features that make them a versatile tool for the statistician: They can be used to derive weak convergence and convergence of moments, and can be easily bounded; they are well-adapted to quantify a natural notion of perturbation of a probability distribution; and they seamlessly incorporate the geometry of the domain of the distributions in question, thus being useful for contrasting complex objects. Consequently, they frequently appear in the development of statistical theory and inferential methodology, and they have recently become an object of inference in themselves. In this review, we provide a snapshot of the main concepts involved in Wasserstein distances and optimal transportation, and a succinct overview of some of their many statistical aspects.

Security and Surveillance in Times of Globalization

2013 ◽  
Vol 2 (4) ◽  
pp. 1-12 ◽  
Author(s):  
Lucas Melgaço
Keyword(s):  
Latin America ◽  
Conceptual Framework ◽  
Theoretical Framework ◽  
Convergence Of Moments ◽  
Urban Security ◽  
Anglo American

Brazilian geographer Milton Santos is among the most influential theorists in Brazil and in the rest of Latin America yet his work has not until now been popularized in Anglo-American scholarship. Santos created a solid theoretical framework composed by a set of articulated concepts, some of which are discussed in this paper: technical-scientific and informational milieu, technical unicity, convergence of moments, enlargement of contexts, knowability of the planet, contemporary acceleration, psycho-sphere, techno-sphere and counter-rationalities. This article also presents Santos' conception of globalization as fable, perversity and possibility. Through a review of the author's main works, particularly the book Toward an Other Globalization, and through the application of some of his concepts to the analysis of contemporary events, this article intends to offer an introduction to Santos to the Anglo world and to demonstrate how his conceptual framework can contribute to the literature on surveillance and urban security.

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