scholarly journals On the Zero-One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment

2005 ◽  
Vol 10 (0) ◽  
pp. 36-44 ◽  
Author(s):  
Firas Rassoul-Agha
Keyword(s):  
Random Walk ◽  
Random Environment ◽  
Law Of Large Numbers ◽  
Large Numbers ◽  
The Law

Random walk in a random environment with correlated sites

2001 ◽  
Vol 38 (4) ◽  
pp. 1018-1032 ◽  
Author(s):  
T. Komorowski ◽  
G. Krupa
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Random Field ◽  
Random Environment ◽  
Law Of Large Numbers ◽  
Transition Probabilities ◽  
Direct Application ◽  
Random Environments ◽  
Large Numbers ◽  
Stationary Random Field

We prove the law of large numbers for random walks in random environments on the d-dimensional integer lattice Zd. The environment is described in terms of a stationary random field of transition probabilities on the lattice, possessing a certain drift property, modeled on the Kalikov condition. In contrast to the previously considered models, we admit possible correlation of transition probabilities at different sites, assuming however that they become independent at finite distances. The possible dependence of sites makes impossible a direct application of the renewal times technique of Sznitman and Zerner.

Random walk in a random environment with correlated sites

2001 ◽  
Vol 38 (04) ◽  
pp. 1018-1032 ◽  
Author(s):  
T. Komorowski ◽  
G. Krupa
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Random Field ◽  
Random Environment ◽  
Law Of Large Numbers ◽  
Transition Probabilities ◽  
Direct Application ◽  
Random Environments ◽  
Large Numbers ◽  
Stationary Random Field

We prove the law of large numbers for random walks in random environments on the d-dimensional integer lattice Z d . The environment is described in terms of a stationary random field of transition probabilities on the lattice, possessing a certain drift property, modeled on the Kalikov condition. In contrast to the previously considered models, we admit possible correlation of transition probabilities at different sites, assuming however that they become independent at finite distances. The possible dependence of sites makes impossible a direct application of the renewal times technique of Sznitman and Zerner.

scholarly journals Tauberian theorems for summability transforms

2005 ◽  
Vol 2005 (1) ◽  
pp. 55-66
Author(s):  
Rohitha Goonatilake
Keyword(s):  
Random Walk ◽  
Rate Of Convergence ◽  
Law Of Large Numbers ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Strong Law ◽  
Random Walk Method ◽  
Large Numbers ◽  
The Law

The convolution summability method is introduced as a generalization of the random-walk method. In this paper, two well-known summability analogs concerning the strong law of large numbers (SLLN) and the law of the single logarithm (LSL), that gives the rate of convergence in SLLN for the random-walk method, are extended to this generalized method.

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
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