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 …

A random walk is a sequence {Sn, n≥ 0} of random variables with independent, identically
distributed (iid) increments {Xk, k≥ 1} and S0= 0. A Bernoulli random walk (also called a …

Many useful descriptions of stochastic models can be obtained from functional limit
theorems (invariance principles or weak convergence theorems for probability measures on …

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its
distributions solve a time-fractional analogue of the Kolmogorov forward equation for a …

Asymptotic expansions are obtained for finite-dimensional symmetric stable distributions.
They are used to prove the existence of continuous transition probability densities of stable …

Our aim here is to give a survey of that part of continuous-time fluctuation theory which can
be approached in terms of functionals of Lévy processes, our principal tools being Wiener …

The monograph is devoted mainly to the analytical study of the differential, pseudo-
differential and stochastic evolution equations describing the transition probabilities of …

Lévy flights are paradigmatic generalised random walk processes, in which the independent
stationary increments—the'jump lengths'—are drawn from an-stable jump length distribution …

INTEGRODIFFERENTIAL EQUATION WHICH INTERPOLATES THE HEAT EQUATION AND
THE WAVE EQUATION (II) (IDE). r ('+i) Γ«"J Page 1 Fujita, Y. Osaka J. Math. 27 (1990), 797-804 …

We first give an interpretation for the conditioning to stay positive (respectively, to die at 0) for
a large class of Lévy processes starting at x> 0. Next, we specify the laws of the pre …