Semistable Lévy Motion

Asymptotic Behavior of Semistable Lévy Exponents and Applications to Fractal Path Properties

This paper proves sharp bounds on the tails of the Lévy exponent of an operator semistable law on Rd . These bounds are then applied to explicitly compute the Hausdorff and packing dimensions of the range, graph, and other random sets describing the sample paths of the corresponding operator semi-selfsimilar Lévy processes. The proofs are elementary, using only the properties of the Lévy expone...

On two multistable extensions of stable Lévy motion and their semimartingale representation

A construction of processes with one-dimensional martingale marginals, associated with a Lévy process, via its Lévy sheet

Abstract We give some adequate extension, in the framework of a general Lévy process, of our previous construction of processes with one-dimensional martingale marginals, done originally in the set-up of Brownian motion. The Lévy process framework allows us to streamline our previous arguments, as well as to reach a larger class of such processes, even in the Brownian case. We give some illustr...

A Combinatorial Method for Calculating the Moments of Lévy Area

We present a new way to compute the moments of the Lévy area of a two-dimensional Brownian motion. Our approach uses iterated integrals and combinatorial arguments involving the shuffle product.

Lévy Processes and Their Subordination in Matrix Lie Groups

Lévy processes in matrix Lie groups are studied. Subordination (random time change) is used to show that quasi-invariance of the Brownian motion in a Lie group induces absolute continuity of the laws of the corresponding pure jump processes. These results are applied to several examples which are discussed in detail. Table of