Some Results of Stable Convergence for Exchangeable Random Variables in Hilbert Spaces

2001 ◽  
Vol 45 (2) ◽  
pp. 329-337
Author(s):  
M. E. Mancino ◽  
L. Pratelli
Keyword(s):  
Hilbert Spaces ◽  
Random Variables ◽  
Stable Convergence ◽  
Exchangeable Random Variables

scholarly journals Some results of stable convergence for exchangeable random variables in Hilbert spaces

2000 ◽  
Vol 45 (2) ◽  
pp. 395-403
Author(s):  
Maria Elvira Mancino ◽  
Maria Elvira Mancino ◽  
Luca Pratelli ◽  
Luca Pratelli
Keyword(s):  
Hilbert Spaces ◽  
Random Variables ◽  
Stable Convergence ◽  
Exchangeable Random Variables

A note on Spitzer's lemma and its application to the maximum of partial sums of dependent random variables

1976 ◽  
Vol 13 (2) ◽  
pp. 361-364 ◽  
Author(s):  
M. E. Solari ◽  
J. E. A. Dunnage
Keyword(s):  
Infinite Sequence ◽  
Random Variables ◽  
Finite Sequence ◽  
Partial Sums ◽  
Dependent Random Variables ◽  
Finite Segment ◽  
Exchangeable Random Variables ◽  
Partial Sum

We give an expression for the expectation of max (0, S1, …, Sn) where Sk is the kth partial sum of a finite sequence of exchangeable random variables X1, …, Xn. When the Xk are also independent, the formula we give has already been obtained by Spitzer; and when the sequence is a finite segment of an infinite sequence of exchangeable random variables, it is a consequence of a theorem of Hewitt.

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.

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