Point Process Convergence and the Circular Beta Ensemble

2020 ◽  
Author(s):  
Eli Cytrynbaum
Keyword(s):  
Point Process ◽  
Beta Ensemble ◽  
Process Convergence

scholarly journals Gumbel and Fréchet convergence of the maxima of independent random walks

2020 ◽  
Vol 52 (1) ◽  
pp. 213-236 ◽  
Author(s):  
Thomas Mikosch ◽  
Jorge Yslas
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Point Process ◽  
Asymptotic Theory ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Independent Random Variables ◽  
Finite Moment ◽  
Process Convergence ◽  
Precise Large Deviation

AbstractWe consider point process convergence for sequences of independent and identically distributed random walks. The objective is to derive asymptotic theory for the largest extremes of these random walks. We show convergence of the maximum random walk to the Gumbel or the Fréchet distributions. The proofs depend heavily on precise large deviation results for sums of independent random variables with a finite moment generating function or with a subexponential distribution.

Point process convergence of stochastic volatility processes with application to sample autocorrelation

2001 ◽  
Vol 38 (A) ◽  
pp. 93-104 ◽  
Author(s):  
Richard A. Davis ◽  
Thomas Mikosch
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Volatility ◽  
Point Process ◽  
Autocorrelation Function ◽  
Linear Models ◽  
Asymptotic Properties ◽  
Infinite Variance ◽  
Bilinear Models ◽  
Process Convergence ◽  
Stochastic Volatility Process

The paper considers one of the standard processes for modeling returns in finance, the stochastic volatility process with regularly varying innovations. The aim of the paper is to show how point process techniques can be used to derive the asymptotic behavior of the sample autocorrelation function of this process with heavy-tailed marginal distributions. Unlike other non-linear models used in finance, such as GARCH and bilinear models, sample autocorrelations of a stochastic volatility process have attractive asymptotic properties. Specifically, in the infinite variance case, the sample autocorrelation function converges to zero in probability at a rate that is faster the heavier the tails of the marginal distribution. This behavior is analogous to the asymptotic behavior of the sample autocorrelations of independent identically distributed random variables.

scholarly journals Convergence to Stable Laws in the Space D

2015 ◽  
Vol 52 (01) ◽  
pp. 1-17 ◽  
Author(s):  
François Roueff ◽  
Philippe Soulier
Keyword(s):  
Point Process ◽  
Regular Variation ◽  
Metric Spaces ◽  
Empirical Process ◽  
Stable Distributions ◽  
Stable Laws ◽  
Random Elements ◽  
Process Convergence ◽  
Reward Process ◽  
Renewal Reward Process

We study the convergence of centered and normalized sums of independent and identically distributed random elements of the spaceDof càdlàg functions endowed with Skorokhod'sJ1topology, to stable distributions inD. Our results are based on the concept of regular variation on metric spaces and on point process convergence. We provide some applications; in particular, to the empirical process of the renewal-reward process.

Point process convergence of stochastic volatility processes with application to sample autocorrelation

2001 ◽  
Vol 38 (A) ◽  
pp. 93-104 ◽  
Author(s):  
Richard A. Davis ◽  
Thomas Mikosch
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Volatility ◽  
Point Process ◽  
Autocorrelation Function ◽  
Linear Models ◽  
Asymptotic Properties ◽  
Infinite Variance ◽  
Bilinear Models ◽  
Process Convergence ◽  
Stochastic Volatility Process

The paper considers one of the standard processes for modeling returns in finance, the stochastic volatility process with regularly varying innovations. The aim of the paper is to show how point process techniques can be used to derive the asymptotic behavior of the sample autocorrelation function of this process with heavy-tailed marginal distributions. Unlike other non-linear models used in finance, such as GARCH and bilinear models, sample autocorrelations of a stochastic volatility process have attractive asymptotic properties. Specifically, in the infinite variance case, the sample autocorrelation function converges to zero in probability at a rate that is faster the heavier the tails of the marginal distribution. This behavior is analogous to the asymptotic behavior of the sample autocorrelations of independent identically distributed random variables.

scholarly journals Convergence to Stable Laws in the SpaceD

2015 ◽  
Vol 52 (1) ◽  
pp. 1-17 ◽  
Author(s):  
François Roueff ◽  
Philippe Soulier
Keyword(s):  
Point Process ◽  
Regular Variation ◽  
Metric Spaces ◽  
Empirical Process ◽  
Stable Distributions ◽  
Stable Laws ◽  
Random Elements ◽  
Process Convergence ◽  
Reward Process ◽  
Renewal Reward Process

We study the convergence of centered and normalized sums of independent and identically distributed random elements of the spaceDof càdlàg functions endowed with Skorokhod'sJ1topology, to stable distributions inD. Our results are based on the concept of regular variation on metric spaces and on point process convergence. We provide some applications; in particular, to the empirical process of the renewal-reward process.

Habitat use of toothed whales in a marine protected area based on point process models

2019 ◽  
Vol 609 ◽  
pp. 239-256 ◽  
Author(s):  
TL Silva ◽  
G Fay ◽  
TA Mooney ◽  
J Robbins ◽  
MT Weinrich ◽  
...  
Keyword(s):  
Habitat Use ◽  
Point Process ◽  
Protected Area ◽  
Marine Protected Area ◽  
Process Models ◽  
Point Process Models
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