Displaying similar documents to “On the rate of approximation in the random sum CLT for dependent variables”

Stochastic ordering of random kth record values

Wiesław Dziubdziela, Agata Tomicka-Stisz (1999)

Applicationes Mathematicae

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Let X 1 , X 2 , . . . be a sequence of independent and identically distributed random variables with continuous distribution function F(x). Denote by X(1,k),X(2,k),... the kth record values corresponding to X 1 , X 2 , . . . We obtain some stochastic comparison results involving the random kth record values X(N,k), where N is a positive integer-valued random variable which is independent of the X i .

Comparing the distributions of sums of independent random vectors

Evgueni I. Gordienko (2005)

Kybernetika

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Let ( X n , n ≥ 1 ) , ( X ˜ n , n ≥ 1 ) be two sequences of i.i.d. random vectors with values in ℝ k and S n = X 1 + ⋯ + X n , S ˜ n = X ˜ 1 + ⋯ + X ˜ n , n ≥ 1 . Assuming that E X 1 = E X ˜ 1 , E | X 1 | 2 < ∞ , E | X ˜ 1 | k + 2 < ∞ and the existence of a density of X ˜ 1 satisfying the certain conditions we prove the following inequalities: v ( S n , S ˜ n ) ≤ c max { v ( X 1 , X ˜ 1 ) , ζ 2 ( X 1 , X ˜ 1 ) } , n = 1 , 2 , ⋯ , where v and ζ 2 are the total variation and Zolotarev’s metrics, respectively.

Limit theorem for random walk in weakly dependent random scenery

Nadine Guillotin-Plantard, Clémentine Prieur (2010)

Annales de l'I.H.P. Probabilités et statistiques

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Let =( )≥0 be a random walk on ℤ and =( )∈ℤ a stationary random sequence of centered random variables, independent of . We consider a random walk in random scenery that is the sequence of random variables ( )≥0, where =∑=0 , ∈ℕ. Under a weak dependence assumption on the scenery we prove a functional limit theorem generalizing Kesten and Spitzer’s [ (1979) 5–25]...