A remark on the law of the logarithm for weighted sums of random variables with multidimensional indices

2011 ◽  
Vol 81 (12) ◽  
pp. 1808-1812 ◽  
Author(s):  
Pingyan Chen ◽  
Chunyan Hao
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Sums Of Random Variables ◽  
Multidimensional Indices ◽  
Law Of The Logarithm ◽  
The Law

Sums and weighted sums of a gamma Markov sequence

1988 ◽  
Vol 25 (01) ◽  
pp. 204-209 ◽  
Author(s):  
Ravindra M. Phatarfod
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Random Variables ◽  
Laplace Transforms ◽  
Weighted Sums ◽  
Sums Of Random Variables ◽  
Markov Sequence

We derive the Laplace transforms of sums and weighted sums of random variables forming a Markov chain whose stationary distribution is gamma. Both seasonal and non-seasonal cases are considered. The results are applied to two problems in stochastic reservoir theory.

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