14 research outputs found
A sharp uniform bound for the distribution of sums of Bernoulli trials
In this note we establish a uniform bound for the distribution of a sum
of independent non-homogeneous Bernoulli trials.
Specifically, we prove that where
denotes the standard deviation of and is a universal
constant. We compute the best possible constant and we show
that the bound also holds for limits of sums and differences of Bernoullis,
including the Poisson laws which constitute the worst case and attain the
bound. We also investigate the optimal bounds for and fixed. An
application to estimate the rate of convergence of Mann's fixed point
iterations is presented.Comment: This paper is a revised version of a previous articl
Topological properties of the solution set of a class of nonlinear evolutions inclusions
summary:In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field , we are able to show that the solution set is in fact an -set. Finally some applications to infinite dimensional control systems are also presented