On the rate of approximation in the random sum CLT for dependent variables

Adhir Kumar Basu

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

Note on successive cumulative sums of independent random variables

Antonín Špaček (1949)

Časopis pro pěstování matematiky a fysiky

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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 $(X_{n}, n \geq 1), ({\tilde{X}}_{n}, n \geq 1)$ be two sequences of i.i.d. random vectors with values in $ℝ^{k}$ and $S_{n} = X_{1} + \dots + X_{n}$ , ${\tilde{S}}_{n} = {\tilde{X}}_{1} + \dots + {\tilde{X}}_{n}$ , $n \geq 1$ . Assuming that $E X_{1} = E {\tilde{X}}_{1}$ , $E | X_{1} |^{2} < \infty$ , $E | {\tilde{X}}_{1} |^{k + 2} < \infty$ and the existence of a density of ${\tilde{X}}_{1}$ satisfying the certain conditions we prove the following inequalities: $v (S_{n}, {\tilde{S}}_{n}) \leq c max {v (X_{1}, {\tilde{X}}_{1}), ζ_{2} (X_{1}, {\tilde{X}}_{1})}, n = 1, 2, \dots,$ 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]...