scholarly journals A Bound for the Law of Large Numbers for Discrete Markov Processes

1961 ◽  
Vol 32 (1) ◽  
pp. 336-337 ◽  
Author(s):  
Melvin Katz ◽  
A. J. Thomasian
Keyword(s):  
Markov Processes ◽  
Law Of Large Numbers ◽  
Large Numbers ◽  
The Law

scholarly journals A new proof for the generalized law of large numbers under Choquet expectation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jing Chen ◽  
Zengjing Chen
Keyword(s):  
Probability Theory ◽  
Law Of Large Numbers ◽  
Moment Condition ◽  
Large Numbers ◽  
Choquet Expectation ◽  
The Law ◽  
Linear Probability ◽  
First Moment ◽  
Independent And Identically Distributed

Abstract In this article, we employ the elementary inequalities arising from the sub-linearity of Choquet expectation to give a new proof for the generalized law of large numbers under Choquet expectations induced by 2-alternating capacities with mild assumptions. This generalizes the Linderberg–Feller methodology for linear probability theory to Choquet expectation framework and extends the law of large numbers under Choquet expectation from the strong independent and identically distributed (iid) assumptions to the convolutional independence combined with the strengthened first moment condition.

Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio

2006 ◽  
Vol 73 (4) ◽  
pp. 673-686 ◽  
Author(s):  
M. A. Milevsky ◽  
S. D. Promislow ◽  
V. R. Young
Keyword(s):  
Mortality Risk ◽  
Law Of Large Numbers ◽  
Sharpe Ratio ◽  
Risk Premiums ◽  
Large Numbers ◽  
The Law

SYNCHRONIZATION IN RANDOMLY DRIVEN SYSTEMS

1995 ◽  
Vol 09 (16) ◽  
pp. 985-988 ◽  
Author(s):  
A.M. JAYANNAVAR
Keyword(s):  
Simple Model ◽  
Law Of Large Numbers ◽  
Driven Systems ◽  
Large Numbers ◽  
Long Time ◽  
The Law

We have solved analytically a simple model of evolution of particles driven by identical noise. We show that the trajectories of all particles collapse into a single trajectory at long time. This synchronization also leads to violation of the law of large numbers.

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