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Martingale transform and Levy Processes on Lie Groups
Martingale transform Levy Processes Lie Groups Probability
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2012/6/29
This paper constructs a class of martingale transforms based on L\'evy processes on Lie groups. From these, a natural class of bounded linear operators on the $L^p$-spaces of the group (with respect t...
Asymptotic behaviour of first passage time distributions for Levy processes
Levy processes first passage time distribution local limit theorems fluctuation theory
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2011/9/19
Abstract: Let $X$ be a real valued L\'evy process that is in the domain of attraction of a stable law without centering with norming function $c.$ As an analogue of the random walk results in \cite{vw...
On the density of exponential functionals of Levy processes
Levy processes exponential functional subordinators self-similar Markov processes
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2011/9/14
Abstract: In this paper, we study the existence of the density associated to the exponential functional of the L\'evy process $\xi$, \[ I_{\ee_q}:=\int_0^{\ee_q} e^{\xi_s} \, \mathrm{d}s, \] where $\e...
Finite Variation of Fractional Levy Processes
finite variation fractional integration fractional L´ evy process
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2011/3/1
Various characterizations for fractional L´evy process to be of finite variation are obtained, one of which is in terms of the characteristic triplet of the driving L´evy process, while ot...