Randomly stopped sums of not identically distributed heavy tailed random variables

2016 ◽  
Vol 113 ◽  
pp. 84-93 ◽  
Author(s):  
Svetlana Danilenko ◽  
Jonas Šiaulys
Keyword(s):  
Random Variables ◽  
Randomly Stopped Sums ◽  
Heavy Tailed ◽  
Stopped Sums

scholarly journals Estimating tails of independently stopped random walks using concave approximations of hazard functions

2021 ◽  
Vol 58 (3) ◽  
pp. 773-793
Author(s):  
Jaakko Lehtomaa
Keyword(s):  
Random Walk ◽  
Asymptotic Analysis ◽  
Sufficient Conditions ◽  
Hazard Functions ◽  
Logarithmic Asymptotics ◽  
Randomly Stopped Sums ◽  
Heavy Tailed ◽  
The Moment ◽  
Stopped Random Walks ◽  
Stopped Sums

AbstractThis paper considers logarithmic asymptotics of tails of randomly stopped sums. The stopping is assumed to be independent of the underlying random walk. First, finiteness of ordinary moments is revisited. Then the study is expanded to more general asymptotic analysis. Results are applicable to a large class of heavy-tailed random variables. The main result enables one to identify if the asymptotic behaviour of a stopped sum is dominated by its increments or the stopping variable. As a consequence, new sufficient conditions for the moment determinacy of compounded sums are obtained.

scholarly journals Improving the Asmussen–Kroese-Type Simulation Estimators

2012 ◽  
Vol 49 (4) ◽  
pp. 1188-1193 ◽  
Author(s):  
Samim Ghamami ◽  
Sheldon M. Ross
Keyword(s):  
Monte Carlo ◽  
Nonnegative Integer ◽  
Rare Event ◽  
Random Variables ◽  
Random Variable ◽  
Heavy Tailed ◽  
Independent Identically Distributed

The Asmussen–Kroese Monte Carlo estimators of P(Sn > u) and P(SN > u) are known to work well in rare event settings, where SN is the sum of independent, identically distributed heavy-tailed random variables X1,…,XN and N is a nonnegative, integer-valued random variable independent of the Xi. In this paper we show how to improve the Asmussen–Kroese estimators of both probabilities when the Xi are nonnegative. We also apply our ideas to estimate the quantity E[(SN-u)+].

scholarly journals Heavy-tailed random matrices

2018 ◽  
Author(s):  
Vladimir Kravtsov
Keyword(s):  
Random Matrices ◽  
Heavy Tails ◽  
Probability Distributions ◽  
Basin Of Attraction ◽  
Random Variables ◽  
Universal Properties ◽  
Random Matrix Ensembles ◽  
Free Random Variables ◽  
Heavy Tailed ◽  
Non Gaussian

This article considers non-Gaussian random matrices consisting of random variables with heavy-tailed probability distributions. In probability theory heavy tails of distributions describe rare but violent events which usually have a dominant influence on the statistics. Furthermore, they completely change the universal properties of eigenvalues and eigenvectors of random matrices. This article focuses on the universal macroscopic properties of Wigner matrices belonging to the Lévy basin of attraction, matrices representing stable free random variables, and a class of heavy-tailed matrices obtained by parametric deformations of standard ensembles. It first examines the properties of heavy-tailed symmetric matrices known as Wigner–Lévy matrices before discussing free random variables and free Lévy matrices as well as heavy-tailed deformations. In particular, it describes random matrix ensembles obtained from standard ensembles by a reweighting of the probability measure. It also analyses several matrix models belonging to heavy-tailed random matrices and presents methods for integrating them.

scholarly journals Moments of Randomly Stopped Sums

1965 ◽  
Vol 36 (3) ◽  
pp. 789-799 ◽  
Author(s):  
Y. S. Chow ◽  
Herbert Robbins ◽  
Henry Teicher
Keyword(s):  
Randomly Stopped Sums ◽  
Stopped Sums
Sign in / Sign up

Export Citation Format

Share Document