On Measure Concentration for Separately Lipschitz Functions in Product Spaces

  • V. Bentkus
  • Published 2006

Abstract

Let Mn = X1 + · · · + Xn be a martingale with bounded differences Xm = Mm −Mm−1 such that P{am − σm ≤ Xm ≤ am + σm} = 1 with nonrandom nonnegative σm and σ(X1, . . . , Xm−1)-measurable random variables am. Write σ2 = σ2 1 +· · ·+σ2 n. Let I(x) = 1−Φ(x), where Φ is the standard normal distribution function. We prove the inequalities P{Mn ≥ x} ≤ cI(x/σ), P{Mn… (More)

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