In applications, and especially in mathematical finance, random time-dependent events are
often modeled as stochastic processes. Assumptions are made about the structure of such …

This paper is concerned with the asymptotic behavior of sums of the form [Formula: see text],
where X is a 1-dimensional semimartingale and fa suitable test function, typically f (x)=| x| r …

In particular, does there exist option pricing rules that are stable under convergence of the
underlying assets (this will reduce the model risk when choosing between discrete time or …

We determine the asymptotic behavior of the realized power variations, and more generally
of sums of a given function f evaluated at the increments of a Lévy process between the …

During the seven years that elapsed between the first and second editions of the present
book, considerable progress was achieved in the area of financial modelling and pricing of …

We consider the approximate Euler scheme for Lévy-driven stochastic differential equations.
We study the rate of convergence in law of the paths. We show that when approximating the …

In this article, we obtain the weak and strong rates of convergence of time integrals of non-
smooth functions of a one dimensional diffusion process. We propose the use of the exact …

We prove that the convolution of a selfdecomposable distribution with its background driving
law is again selfdecomposable if and only if the background driving law is s …

We provide a simple algorithm for construction of Brownian paths approximating those of a
Lévy process on a finite time interval. It requires knowledge of the Lévy process trajectory on …

The approximation of integral type functionals is studied for discrete observations of a
continuous It\^ o semimartingale. Based on novel approximations in the Fourier domain …