Asymptotic expansions for functionals of a Poisson random measure

Poisson approximations for functionals of random trees

We use Poisson approximation techniques for sums of indicator random variables to derive explicit error bounds and central limit theorems for several functionals of random trees. In particular, we consider (i) the number of comparisons for successful and unsuccessful search in a binary search tree and (ii) internode distances in increasing trees. The Poisson approximation setting is shown to be...

Multiple stochastic integral expansions of arbitrary Poisson jump times functionals

We compute the Wiener-Poisson expansion of square-integrable functionals of a nite number of Poisson jump times in series of multiple Poisson stochastic integrals.

Zero bias transformation and asymptotic expansions II : the Poisson case

We apply a discrete version of the methodology in [12] to obtain a recursive asymptotic expansion for E[h(W )] in terms of Poisson expectations, where W is a sum of independent integer-valued random variables and h is a polynomially growing function. We also discuss the remainder estimations. MSC 2000 subject classifications: 60G50, 60F05.

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

Second Order Moment Asymptotic Expansions for a Randomly Stopped and Standardized Sum

This paper establishes the first four moment expansions to the order o(a^−1) of S_{t_{a}}^{prime }/sqrt{t_{a}}, where S_{n}^{prime }=sum_{i=1}^{n}Y_{i} is a simple random walk with E(Yi) = 0, and ta is a stopping time given by t_{a}=inf left{ ngeq 1:n+S_{n}+zeta _{n}>aright}‎ where S_{n}=sum_{i=1}^{n}X_{i} is another simple random walk with E(Xi) = 0, and {zeta _{n},ngeq 1} is a sequence of ran...