scholarly journals Sharp inequality for randomly stopped sums of independent non-negative random variables

1994 ◽  
Vol 51 (1) ◽  
pp. 63-73 ◽  
Author(s):  
Paweʖl Hitczenko
Keyword(s):  
Random Variables ◽  
Sharp Inequality ◽  
Randomly Stopped Sums ◽  
Stopped Sums

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 the Joint Distribution of Stopping Times and Stopped Sums in Multistate Exchangeable Trials

2014 ◽  
Vol 51 (2) ◽  
pp. 483-491 ◽  
Author(s):  
M. V. Boutsikas ◽  
D. L. Antzoulakos ◽  
A. C. Rakitzis
Keyword(s):  
Joint Distribution ◽  
Stopping Time ◽  
Random Variables ◽  
Stopping Times ◽  
Independent Interest ◽  
Exchangeable Random Variables ◽  
Stopped Sums ◽  
Independent And Identically Distributed

Let T be a stopping time associated with a sequence of independent and identically distributed or exchangeable random variables taking values in {0, 1, 2, …, m}, and let ST,i be the stopped sum denoting the number of appearances of outcome 'i' in X1, …, XT, 0 ≤ i ≤ m. In this paper we present results revealing that, if the distribution of T is known, then we can also derive the joint distribution of (T, ST,0, ST,1, …, ST,m). Two applications, which have independent interest, are offered to illustrate the applicability and the usefulness of the main results.

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

On a conjecture for the non-existence of the expectation of randomly stopped sums

1995 ◽  
Vol 32 (4) ◽  
pp. 1138-1141
Author(s):  
Claude Lefèvre ◽  
Sergey Utev
Keyword(s):  
Positive Answer ◽  
Randomly Stopped Sums ◽  
Stopped Sums

In a recent paper on the validity of Wald's equation, Roters (1994) raised an important question on the non-existence of the expectation of randomly stopped sums. The purpose of this note is to answer the question in the affirmative. As a consequence, an old question by Taylor (1972) also gets a positive answer.

scholarly journals Asymptotics of randomly stopped sums in the presence of heavy tails

Bernoulli ◽  
2010 ◽  
Vol 16 (4) ◽  
pp. 971-994 ◽  
Author(s):  
Denis Denisov ◽  
Serguei Foss ◽  
Dmitry Korshunov
Keyword(s):  
Heavy Tails ◽  
Randomly Stopped Sums ◽  
Stopped Sums
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