A note on vague convergence of measures

Univariate heavy-tailed analysis rests on the analytic notion of regularly varying functions. For multivariate heavy-tailed analysis, reliance on functions is awkward because multivariate distribution functions are not natural objects for many purposes and are difficult to manipulate. An approach based on vague convergence of measures makes the differences between univariate and multivariate analysis evaporate. We survey the foundations of the subject and discuss statistical attempts to assess dependence of large values. An exploratory technique is applied to exchange rate return data and shows clear differences in the dependence structure of large values for the Japanese Yen versus German Mark compared with the French Franc versus the German Mark.

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Markov Chains Conditioned Never to Wait Too Long at the Origin

Journal of Applied Probability ◽

10.1017/s0021900200005891 ◽

2009 ◽

Vol 46 (03) ◽

pp. 812-826

Author(s):

Saul Jacka

Keyword(s):

Markov Chain ◽

Markov Chains ◽

State Space ◽

Sufficient Conditions ◽

Weak Limit ◽

The State ◽

Coin Tossing ◽

First Time ◽

Vague Convergence ◽

Irreducible Markov Chain

Motivated by Feller's coin-tossing problem, we consider the problem of conditioning an irreducible Markov chain never to wait too long at 0. Denoting by τ the first time that the chain,X, waits for at least one unit of time at the origin, we consider conditioning the chain on the event (τ›T). We show that there is a weak limit asT→∞ in the cases where either the state space is finite orXis transient. We give sufficient conditions for the existence of a weak limit in other cases and show that we have vague convergence to a defective limit if the time to hit zero has a lighter tail than τ and τ is subexponential.

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Vague convergence of locally integrable martingale measures

Stochastic Processes and their Applications ◽

10.1016/0304-4149(94)90025-6 ◽

1994 ◽

Vol 52 (2) ◽

pp. 211-227 ◽

Cited By ~ 3

Author(s):

Yingchao Xie

Keyword(s):

Martingale Measures ◽

Integrable Martingale ◽

Vague Convergence

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On Vague Convergence of Stochastic Processes

The Annals of Probability ◽

10.1214/aop/1176996227 ◽

1975 ◽

Vol 3 (6) ◽

pp. 1014-1022

Author(s):

R. V. Erickson ◽

Vaclav Fabian

Keyword(s):

Stochastic Processes ◽

Vague Convergence

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Uniformity in Weak and Vague Convergence

Theory of Probability and Its Applications ◽

10.1137/1130069 ◽

1986 ◽

Vol 30 (3) ◽

pp. 573-576 ◽

Cited By ~ 1

Author(s):

S. T. Rachev

Keyword(s):

Vague Convergence

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The Second Screen: Convergence as Crisis

Zeitschrift für Medien- und Kulturforschung ◽

10.28937/1000106448 ◽

2015 ◽

Vol 6 (2) ◽

pp. 123-144 ◽

Cited By ~ 5

Author(s):

Markus Stauff

Keyword(s):

Smart Phones ◽

Tablet Computers ◽

Second Screen ◽

Starting Point ◽

Multiple Devices ◽

Vague Convergence

Dieser Artikel nimmt den >zweiten Bildschirm< – TV-bezogene Nutzung von Smartphones und Tablets – zum Ausgangspunkt, um die immer heterogeneren Verbindungen zwischen mehreren Geräten, Texten und Plattformen zu diskutieren, von denen die zeitgenössische Kultur geformt wird. Sie bilden instabile Assemblagen, die die spezifischen affordances (Aufforderungscharaktere) ihrer Elemente gleichzeitig hervorheben und untergraben. Indem der Fokus zunächst auf technische und industrielle, sodann auf praktische und heimische Verfahren der Herstellung von Verbindungen gelegt wird, wird die aktuelle Medienlandschaft als »Konvergenz in der Krise« beschrieben: Während Medien in der Tat immer mehr miteinander verbunden werden, bleiben die Verbindungen selbst und die Form der Montage in ihrer Gänze flüchtig, instabil und vage. Konvergenz entsteht und besteht als In-der-Krise-sein. </br></br>This article takes the second screen – television-related use of smart phones and tablet computers – as a starting point to discuss how current culture is shaped by the ever more heterogeneous connections between multiple devices, texts and platforms. They form unstable assemblages that simultaneously highlight and undermine the specific affordances of their elements. Focusing first on technical and industrial and then on practical and domestic procedures of creating connections, the current media landscape will be described as >convergence as crisis<: While media indeed become increasingly more interconnected, the connections themselves and the shape of the assemblage in its entirety are ephemeral, unstable and vague. Convergence mainly exists and is generated through being in crisis.

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