Author:
Asmussen Søren,Rosiński Jan
Abstract
Let X = (X(t):t ≥ 0) be a Lévy process and X
∊ the compensated sum of jumps not exceeding ∊ in absolute value, σ2(∊) = var(X
∊(1)). In simulation, X - X
∊ is easily generated as the sum of a Brownian term and a compound Poisson one, and we investigate here when X
∊/σ(∊) can be approximated by another Brownian term. A necessary and sufficient condition in terms of σ(∊) is given, and it is shown that when the condition fails, the behaviour of X
∊/σ(∊) can be quite intricate. This condition is also related to the decay of terms in series expansions. We further discuss error rates in terms of Berry-Esseen bounds and Edgeworth approximations.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
175 articles.
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