Fractional Edgeworth expansions for one-dimensional heavy-tailed random variables and applications

2021/01/05 by Chiarini, Leandro, Jara, Milton, Ruszel, Wioletta M. · 1 citation
#60E07 #60E10 #60F05 #60G50 #60G52 #60J45 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2101.01609

Abstract

In this article, we study a class of lattice random variables in the domain of attraction of an α-stable random variable with index α∈ (0,2) which satisfy a truncated fractional Edgeworth expansion. Our results include studying the class of such fractional Edgeworth expansions under simple operations, providing concrete examples; sharp rates of convergence to an α-stable distribution in a local central limit theorem; Green's function expansions; and finally fluctuations of a class of discrete stochastic PDE's driven by the heavy-tailed random walks belonging to the class of fractional Edgeworth expansions.

Cited by

• Sharp asymptotics for N-point correlation functions of coalescing heavy-tailed random walk

Related

• Non-uniform Edgeworth expansions for weakly dependent random variables and their applications
• Edgeworth expansions for independent bounded integer valued random variables
• Ruin probabilities in tough times - Part 2 - Heavy-traffic approximation for fractionally differentiated random walks in the domain of attraction of a nonGaussian stable distribution
• Ruin probabilities in tough times - Part 1 - Heavy-traffic approximation for fractionally integrated random walks in the domain of attraction of a nonGaussian stable distribution
• Non-Uniform Bounds in Local Limit Theorems in Case of Fractional Moments