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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...
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...
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...
Various characterizations for fractional 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...
We study the distribution and various properties of exponential functionals of hypergeometric L´evy processes. We derive an explicit formula for the Mellin transform of the exponential function...
We derive explicit formulas for the Mellin transform and the distribution of the exponential functional for Levy processes with rational Laplace exponent. This extends recent results by Cai and Kou o...
n this paper we introduce homogeneous multiplicative functionals of Levy processes and investigate their bivariate Revuz measures. We also prove that the sector condition will be inherited by suly-Lvy...
In this paper we show that a path-wise solution to the following integral equation $$ Y_t = \int_0^t f(Y_t) dX_t \qquad Y_0=a \in \R^d $$ exists under the assumption that X_t is a L\'evy process of f...
We prove that the stochastic differential equation $$ Y_{s,t}(x) = Y_{s,s}(x) + \int_0^{t-s} f(Y_{s,s+u}(x)) dX_{s+u}, Y_{s,s}(x)=x\in\R^d. $$ driven by a L\'evy process whose paths have finite p-va...

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