Displaying similar documents to “Large deviations for independent random variables – Application to Erdös-Renyi’s functional law of large numbers”

Complete q -order moment convergence of moving average processes under ϕ -mixing assumptions

Xing-Cai Zhou, Jin-Guan Lin (2014)

Applications of Mathematics

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Let { Y i , - < i < } be a doubly infinite sequence of identically distributed ϕ -mixing random variables, and { a i , - < i < } an absolutely summable sequence of real numbers. We prove the complete q -order moment convergence for the partial sums of moving average processes X n = i = - a i Y i + n , n 1 based on the sequence { Y i , - < i < } of ϕ -mixing random variables under some suitable conditions. These results generalize and complement earlier results.

Dominant eigenvalue problem for positive integral operators and its solution by Monte Carlo method

Jan Kyncl (1998)

Applications of Mathematics

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In this paper, a method of numerical solution to the dominant eigenvalue problem for positive integral operators is presented. This method is based on results of the theory of positive operators developed by Krein and Rutman. The problem is solved by Monte Carlo method constructing random variables in such a way that differences between results obtained and the exact ones would be arbitrarily small. Some numerical results are shown.