4 papers · 1 filter
Measuring the magnitude of sums of independent random variables
Pawel Hitczenko, Stephen Montgomery-Smith
This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy…
A comparison inequality for sums of independent random variables
Stephen Montgomery-Smith, Alexander R. Pruss
We give a comparison inequality that allows one to estimate the tail probabilities of sums of independent Banach space valued random variables in terms of those of independent iden…
Concrete representation of martingales
Stephen J. Montgomery-Smith
Let (f_n) be a mean zero vector valued martingale sequence. Then there exist vector valued functions (d_n) from [0,1]^n such that int_0^1 d_n(x_1,...,x_n) dx_n = 0 for almost all x…
A note on sums of independent random variables
Paweł Hitczenko, Stephen Montgomery-Smith
In this note a two sided bound on the tail probability of sums of independent, and either symmetric or nonnegative, random variables is obtained. We utilize a recent result by Lata…