Oscillation of modes of some semi-stable Lévy processes

Fractional transport equations for Lévy stable processes.

The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a system subjected to a Lévy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limits of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the f...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Conditioned stable Lévy processes and Lamperti representation . February 2 , 2008

By killing a stable Lévy process when it leaves the positive half-line, or by conditioning it to stay positive, or by conditioning it to hit 0 continuously, we obtain three different positive self-similar Markov processes which illustrate the three classes described by Lamperti [10]. For each of these processes, we compute explicitly the infinitesimal generator from which we deduce the characte...

Basics of Lévy Processes *

This is a draft Chapter from a book by the authors on “Lévy Driven Volatility Models”.

Some Peculiar Semi-markov Processes