Strong laws for randomly weighted sums of random variables and applications in the bootstrap and random design regression

2019 ◽  
Author(s):  
Pingyan Chen ◽  
Tao Zhang ◽  
Soo Hak Sung
Keyword(s):  
Random Variables ◽  
Weighted Sums ◽  
Random Design ◽  
Strong Laws ◽  
Sums Of Random Variables ◽  
Randomly Weighted Sums

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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