A Law of the Iterated Logarithm for Randomly Stopped Sums of Heavy Tailed Random Vectors

2000 ◽  
Vol 130 (4) ◽  
pp. 329-347 ◽  
Author(s):  
Hans-Peter Scheffler ◽  
Peter Becker-Kern
Keyword(s):  
Random Vectors ◽  
Iterated Logarithm ◽  
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 Large deviation probabilities for sums of heavy-tailed dependent random vectors

1997 ◽  
Vol 13 (4) ◽  
pp. 647-660 ◽  
Author(s):  
Adam Jakubowski ◽  
Alexander. V. Nagaev ◽  
Zaigraev Alexander
Keyword(s):  
Large Deviation ◽  
Random Vectors ◽  
Large Deviation Probabilities ◽  
Heavy Tailed

scholarly journals The law of the iterated logarithm on subsequences-characterizations

1990 ◽  
Vol 118 ◽  
pp. 65-97 ◽  
Author(s):  
Michel Weber
Keyword(s):  
Unit Ball ◽  
Covariance Matrix ◽  
Identity Matrix ◽  
Random Vectors ◽  
Unbounded Function ◽  
Iterated Logarithm ◽  
Cluster Set ◽  
Euclidian Space ◽  
Zero Vector ◽  
Increasing Sequences

Let be any increasing sequence of integers and M> 1; we connect to them in a very simply way, an increasing unbounded function φ: → R+. Let also X1, X2, · · · be a sequence of i.i.d. random vectors with value in euclidian space Rm. We prove that the cluster set of the sequence almost surely coincides with the unit ball of Rm, if, and only if, the covariance matrix of X1 is the identity matrix of Rm and EX1 is the zero vector of Rm. We define a functional A on the set of increasing sequences of integers as follows:.

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

scholarly journals On lower limits and equivalences for distribution tails of randomly stopped sums

Bernoulli ◽  
2008 ◽  
Vol 14 (2) ◽  
pp. 391-404 ◽  
Author(s):  
Denis Denisov ◽  
Serguei Foss ◽  
Dmitry Korshunov
Keyword(s):  
Randomly Stopped Sums ◽  
Lower Limits ◽  
Stopped Sums
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