Optimal two-value zero-mean disintegration of zero-mean random variables.
“Non-strict" L'Hospital-Type rules for monotonicity: intervals of constancy.
On l'Hospital-type rules for monotonicity.
On normal domination of (super)martingales.
L'Hospital-type rules for monotonicity, and the Lambert and Saccheri quadrilaterals in hyperbolic geometry.
L'Hospital type rules for monotonicity: Applications to probability inequalities for sums of bounded random variables.
Monotonicity properties of the relative error of a Padé approximation for Mills' ratio.
L'Hospital type rules for oscillation, with applications.
L'Hospital type results for monotonicity, with applications.
Exponential deficiency of convolutions of densities
If a probability density (x) (x ∈ ℝ) is bounded and := ∫e (x)dx < ∞ for some linear functional u and all ∈ (01), then, for each ∈ (01) and all large enough , the -fold convolution of the -tilted density ˜pt := e (x)/ is bounded. This is a corollary of a general, “non-i.i.d.” result, which is also shown to enjoy a certain optimality property. Such results and their corollaries stated in terms of the absolute integrability of the corresponding characteristic...
A topological dichotomy with applications to complex analysis
Let X be a compact topological space, and let D be a subset of X. Let Y be a Hausdorff topological space. Let f be a continuous map of the closure of D to Y such that f(D) is open. Let E be any connected subset of the complement (to Y) of the image f(∂D) of the boundary ∂D of D. Then f(D) either contains E or is contained in the complement of E. Applications of this dichotomy principle are given, in particular for holomorphic maps, including maximum and minimum modulus principles,...
On the Bennett–Hoeffding inequality
The well-known Bennett–Hoeffding bound for sums of independent random variables is refined, by taking into account positive-part third moments, and at that significantly improved by using, instead of the class of all increasing exponential functions, a much larger class of generalized moment functions. The resulting bounds have certain optimality properties. The results can be extended in a standard manner to (the maximal functions of) (super)martingales. The proof of the main result relies on an...
Exponential deficiency of convolutions of densities
If a probability density () ( ∈ ℝ) is bounded and := ∫e ()d < ∞ for some linear functional and all ∈ (01), then, for each ∈ (01) and all large enough , the -fold convolution of the -tilted density := e ()/ is bounded. This is a corollary of a general, “non-i.i.d.” result, which is also shown to enjoy a certain optimality property. Such results and their corollaries stated in terms of the absolute integrability of the corresponding characteristic functions...
Toward the best constant factor for the Rademacher-Gaussian tail comparison
It is proved that the best constant factor in the Rademacher-Gaussian tail comparison is between two explicitly defined absolute constants and such that 1.01 . A discussion of relative merits of this result limit theorems is given.
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