Almost surely convergent summands of a random sum

2012 ◽  
Vol 82 (1) ◽  
pp. 212-216 ◽  
Author(s):  
S. Chobanyan ◽  
S. Levental ◽  
V. Mandrekar
Keyword(s):  
Random Sum

The tail behaviour of a random sum of subexponential random variables and vectors

Extremes ◽  
2007 ◽  
Vol 10 (1-2) ◽  
pp. 21-39 ◽  
Author(s):  
D. J. Daley ◽  
Edward Omey ◽  
Rein Vesilo
Keyword(s):  
Random Variables ◽  
Random Sum ◽  
Tail Behaviour

Large deviations of heavy-tailed random sums with applications in insurance and finance

1997 ◽  
Vol 34 (2) ◽  
pp. 293-308 ◽  
Author(s):  
C. Klüppelberg ◽  
T. Mikosch
Keyword(s):  
Distribution Function ◽  
Large Deviation ◽  
Random Variables ◽  
Compound Poisson Process ◽  
Random Sum ◽  
Random Sums ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Heavy Tailed ◽  
The Right

We prove large deviation results for the random sum , , where are non-negative integer-valued random variables and are i.i.d. non-negative random variables with common distribution function F, independent of . Special attention is paid to the compound Poisson process and its ramifications. The right tail of the distribution function F is supposed to be of Pareto type (regularly or extended regularly varying). The large deviation results are applied to certain problems in insurance and finance which are related to large claims.

scholarly journals Random sum-free subsets of abelian groups

2013 ◽  
Vol 199 (2) ◽  
pp. 651-685 ◽  
Author(s):  
József Balogh ◽  
Robert Morris ◽  
Wojciech Samotij
Keyword(s):  
Abelian Groups ◽  
Random Sum

On the distance between the distributions of random sums

2003 ◽  
Vol 40 (01) ◽  
pp. 87-106 ◽  
Author(s):  
Bero Roos ◽  
Dietmar Pfeifer
Keyword(s):  
Total Variation ◽  
Approximation Problem ◽  
Upper Bounds ◽  
Total Variation Distance ◽  
Random Sum ◽  
Random Sums ◽  
Random Summation ◽  
Variation Distance ◽  
Stop Loss

In this paper, we consider the total variation distance between the distributions of two random sums S M and S N with different random summation indices M and N. We derive upper bounds, some of which are sharp. Further, bounds with so-called magic factors are possible. Better results are possible when M and N are stochastically or stop-loss ordered. It turns out that the solution of this approximation problem strongly depends on how many of the first moments of M and N coincide. As approximations, we therefore choose suitable finite signed measures, which coincide with the distribution of the approximating random sum S N if M and N have the same first moments.

On the structure of a random sum-free set

1987 ◽  
Vol 76 (4) ◽  
pp. 523-531 ◽  
Author(s):  
Peter J. Cameron
Keyword(s):  
Random Sum ◽  
Free Set
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