Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

Exponential functionals of Le19 evy processes Page 1 Probability Surveys Vol. 2 (2005) 191–212
ISSN: 1549-5787 DOI: 10.1214/154957805100000122 Exponential functionals of Lévy …

Motivated by recent studies in financial mathematics and other areas, we investigate the
exponential functional Z=∫ 0∞ eX (t) dt of a Lévy process X (t), t⩾ 0. In particular, we …

In this work we analyse the solution to the recurrence equation M_Ψ(z+1)=-zΨ(-
z)M_Ψ(z),\quadM_Ψ(1)=1, defined on a subset of the imaginary line and where -Ψ is any …

Stable Lévy processes lie at the intersection of Lévy processes and self-similar Markov
processes. Processes in the latter class enjoy a Lamperti-type representation as the space …

We study the distribution and various properties of exponential functionals of
hypergeometric Lévy processes. We derive an explicit formula for the Mellin transform of the …

By variously killing a stable Lévy process when it leaves the positive half-line, conditioning it
to stay positive, and conditioning it to hit 0 continuously, we obtain three different, positive …

The generalised Ornstein–Uhlenbeck process constructed from a bivariate Lévy process (ξt,
ηt) t⩾ 0 is defined aswhere V0 is an independent starting random variable. The stationarity …

We compare the probabilistic properties of the non-Gaussian Ornstein–Uhlenbeck based
stochastic volatility model of Barndorff-Nielsen and Shephard (2001) with those of the …