scholarly journals General Limit Theorems with $o$-Rates and Markov Processes under Pseudo-Moment Conditions

1988 ◽  
Vol 7 (4) ◽  
pp. 289-307 ◽  
Author(s):  
Paul Butzer ◽  
Heribert Kirschfink
Keyword(s):  
Markov Processes ◽  
Limit Theorems ◽  
Moment Conditions ◽  
General Limit

scholarly journals Central limit theorems for supercritical branching Markov processes

2014 ◽  
Vol 266 (3) ◽  
pp. 1716-1756 ◽  
Author(s):  
Yan-Xia Ren ◽  
Renming Song ◽  
Rui Zhang
Keyword(s):  
Central Limit ◽  
Markov Processes ◽  
Limit Theorems ◽  
Central Limit Theorems

scholarly journals Limit Theorems for Reversible Markov Processes

1973 ◽  
Vol 1 (6) ◽  
pp. 1014-1025
Author(s):  
Michael L. Levitan ◽  
Lawrence H. Smolowitz
Keyword(s):  
Markov Processes ◽  
Limit Theorems ◽  
Reversible Markov Processes

scholarly journals A Note on Rényi's ‘Record’ Problem and Engel's Series

2018 ◽  
Vol 61 (2) ◽  
pp. 363-369 ◽  
Author(s):  
Lulu Fang ◽  
Min Wu
Keyword(s):  
Number Theory ◽  
Large Deviations ◽  
Markov Processes ◽  
Classical Limit ◽  
Limit Theorems ◽  
London Math ◽  
Law Of Large Numbers ◽  
Record Times ◽  
Iterated Logarithm ◽  
Large Numbers

AbstractIn 1973, Williams [D. Williams, On Rényi's ‘record’ problem and Engel's series, Bull. London Math. Soc.5 (1973), 235–237] introduced two interesting discrete Markov processes, namely C-processes and A-processes, which are related to record times in statistics and Engel's series in number theory respectively. Moreover, he showed that these two processes share the same classical limit theorems, such as the law of large numbers, central limit theorem and law of the iterated logarithm. In this paper, we consider the large deviations for these two Markov processes, which indicate that there is a difference between C-processes and A-processes in the context of large deviations.

scholarly journals The Coupon Collector's Problem Revisited: Asymptotics of the Variance

2012 ◽  
Vol 44 (1) ◽  
pp. 166-195 ◽  
Author(s):  
Aristides V. Doumas ◽  
Vassilis G. Papanicolaou
Keyword(s):  
Large Class ◽  
Limit Distribution ◽  
Limit Theorems ◽  
Gumbel Distribution ◽  
Coupon Collector’S Problem ◽  
Second Moments ◽  
General Limit ◽  
Coupon Collector's Problem

We develop techniques for computing the asymptotics of the first and second moments of the number TN of coupons that a collector has to buy in order to find all N existing different coupons as N → ∞. The probabilities (occurring frequencies) of the coupons can be quite arbitrary. From these asymptotics we obtain the leading behavior of the variance V[TN] of TN (see Theorems 3.1 and 4.4). Then, we combine our results with the general limit theorems of Neal in order to derive the limit distribution of TN (appropriately normalized), which, for a large class of probabilities, turns out to be the standard Gumbel distribution. We also give various illustrative examples.

Sign in / Sign up

Export Citation Format

Share Document