The Malliavin-Stein Method for Normal Random Walks with Dependent Increments

Journal of stochastic analysis(2023)

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Abstract
We derive bounds on the Kolmogorov distance between the distribution of a random functional of a {0, 1}-valued random sequence and the normal distribution.Our approach, which relies on the general framework of stochastic analysis for discrete-time normal martingales, extends existing results obtained for independent Bernoulli (or Rademacher) sequences.In particular, we obtain Kolmogorov distance bounds for the sum of normalized random sequences without any independence assumption.
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Key words
normal random walks,random walks,malliavin-stein
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