Law of Large Numbers and Central Limit Theorem Under Probability Uncertainty

2019 ◽  
pp. 23-45
Author(s):  
Shige Peng
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
Large Numbers

scholarly journals The time to absorption in Λ-coalescents

2018 ◽  
Vol 50 (A) ◽  
pp. 177-190
Author(s):  
Götz Kersting ◽  
Anton Wakolbinger
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Counting Process ◽  
Law Of Large Numbers ◽  
Large Numbers

Abstract We present a law of large numbers and a central limit theorem for the time to absorption of Λ-coalescents with dust started from n blocks, as n→∞. The proofs rely on an approximation of the logarithm of the block-counting process by means of a drifted subordinator.

Central limit theorem and the law of large numbers

1981 ◽  
Vol 30 (4) ◽  
pp. 786-791
Author(s):  
V. M. Kruglov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
Large Numbers ◽  
The Law

Waitingtimes between record observations

1967 ◽  
Vol 4 (01) ◽  
pp. 206-208 ◽  
Author(s):  
Marcel F. Neuts
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Asymptotic Normality ◽  
Central Limit ◽  
Law Of Large Numbers ◽  
Continuous Distribution ◽  
Random Variables ◽  
Large Numbers ◽  
Upper Record ◽  
Independent Identically Distributed

If Δ r denotes the waitingtime between the (r − 1)st and the rth upper record in a sequence of independent, identically distributed random variables with a continuous distribution, then it is shown that Δ r satisfies the weak law of large numbers and a central limit theorem. This theorem supplements those of Foster and Stuart and Rényi, who investigated the index Vr of the rth upper record. Qualitatively the theorems establish the intuitive fact that for higher records, the waitingtime between the last two records outweighs even the total waitingtime for previous records. This explains also why the asymptotic normality of logVr is very inadequate for approximation purposes—Barton and Mallows.

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