Generalised two-sample U-statistics and a two-species reaction-diffusion model

Mathew D. Penrose

Stochastic Processes and their Applications, 1995, vol. 55, issue 1, 57-64

Abstract: Consider a random variable of the form U = [summation operator] f(Xi, Yj), where the sum is over all pairs from independent samples (X1, ..., Xn) and (Y1, ..., Ym) from two (possibly different) distributions, and f is a given function which may depend on n. We discuss possible limits for the distribution of U when n becomes large with n/(m+n) approaching a fixed limit. We discuss an application to a Brownian motion for the irreversible two-species, diffusion-controlled chemical reaction.

Keywords: U-statistics; Limit; laws; Infinitely; divisible; distributions; Chemistry; Reaction; Diffusion; Brownian; motion; Poisson; process (search for similar items in EconPapers)
Date: 1995
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