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.

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

1995 ◽  
Vol 32 (04) ◽  
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 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

scholarly journals Local probabilities of randomly stopped sums of power-law lattice random variables

2019 ◽  
Vol 59 (4) ◽  
pp. 437-468
Author(s):  
Mindaugas Bloznelis
Keyword(s):  
Power Law ◽  
Random Variables ◽  
Randomly Stopped Sums ◽  
Stopped Sums

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

Higher Moments of Randomly Stopped Sums

1966 ◽  
Vol 11 (1) ◽  
pp. 160-165 ◽  
Author(s):  
H. Teicher
Keyword(s):  
Higher Moments ◽  
Randomly Stopped Sums ◽  
Stopped Sums

On Wald's equations in continuous time

1970 ◽  
Vol 7 (1) ◽  
pp. 59-68 ◽  
Author(s):  
W. J. Hall
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Stopping Time ◽  
Wiener Processes ◽  
Independent Increments ◽  
Randomly Stopped Sums ◽  
Continuous Time Processes ◽  
Wald's Identity ◽  
Stopped Sums ◽  
Inequality Theorem

Various formulas of Wald relating to randomly stopped sums have well known continuous-time analogs, holding in particular for Wiener processes. However, sufficiently general forms of most of these do not appear explicitly in the literature. Recent papers by Robbins and Samuel (1966) and by Brown (1969) provide general results on Wald's equations in discrete time and these are here extended (Theorems 2 and 3) to Wiener processes and other homogeneous additive processes, that is, continuous-time processes with stationary independent increments. We also give an inequality (Theorem 1) related to Wald's identity in continuous time, and we derive, as corollaries of Wald's equations, bounds on the variance of an arbitrary stopping time. The Wiener process versions of these results find application in a variety of stopping problems. Specifically, all are used in Hall ((1968), (1969)); see also Bechhofer, Kiefer, and Sobel (1968), Root (1969), and Shepp (1967).

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
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