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Approximating Sums Of Products Of Dependent Random Variables

Leslaw Gajek, Elżbieta Krajewska
Published 2020 · Mathematics

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Abstract Stochastic approximation of a given time series { ∑ j = 1 k X j Y j } by a linear combination of simpler sequences { ∑ j = 1 k X j } and { ∑ j = 1 k Y j } is treated uniformly over k ∈ { 1 , … , n } . A maximal inequality is proven in order to find a sharp bound on Value-at-Risk of max 1 ≤ k ≤ n | ∑ j = 1 k X j Y j | .
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