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- W4384786019 abstract "Let (Xn,j) and (Yn,j) be two arrays of real random variables and f:R→R a Borel function. Define Dn= ∑jf(∑i=1j−1Yn,i)Xn,j and D=Z ∫01f2(BG(t))dF(t) where B is a standard Brownian motion, Z a standard normal random variable independent of B, and F and G are distribution functions. Conditions for Dn→D, in distribution or stably, are given. Among other things, such conditions apply to certain sequences of stochastic integrals, when the quadratic variations of the integrand processes converge in distribution but not in probability. An upper bound for the Wasserstein distance between the probability distributions of Dn and D is obtained as well." @default.
- W4384786019 created "2023-07-20" @default.
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- W4384786019 date "2023-01-01" @default.
- W4384786019 modified "2023-09-26" @default.
- W4384786019 title "A central limit theorem for some generalized martingale arrays" @default.
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- W4384786019 doi "https://doi.org/10.1214/23-ecp534" @default.
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