A comparison inequality for sums of independent random variables
Stephen Montgomery-Smith, Alexander R. Pruss
Abstract
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 identically distributed random variables. More precisely, let X1,...,Xn be independent Banach-valued random variables. Let I be a random variable independent of X1,...,Xn and uniformly distributed over 1,...,n. Put Z1 = XI, and let Z2,...,Zn be independent identically distributed copies of Z1. Then, P(||X1+...+Xn|| > t) < c P(||Z1+...+Zn|| > t/c), for all t>0, where c is an absolute constant.
Create a lesson
Related papers
Sandpile avalanches in two dimensions are finite
Ahmed Bou-Rabee
Markov Chain Convergence in Kernel-Induced Geometry
Oleksii Kachaiev, Luc Brogat-Motte, Silvia Villa et al.
Interacting Stochastic Systems with Agent-Based Sampling and Connection-Based Reinforcement
Yogesh Dahiya, Gursharn Kaur, Neeraja Sahasrabudhe
Dimension-free Markov--Bernstein-type inequality for R2-valued polynomials
Egor Kosov
Initialization-Dependent Solution Selection by the Euler-Maruyama Scheme for a Degenerate SDE
Akihiro Tanaka
Statistical inference for rough Burgers-type stochastic partial differential equations
Simon Chony Acosta Christian Olivera Ciprian Tudor