Articlebronze2009

Conditions for the existence and smoothness of the distribution density of the Ornstein–Uhlenbeck process with Lévy noise

22 citations0/0 files storedTheory of Probability and Mathematical Statistics

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Stochastic processes and financial applications Probability and Statistical Research Stochastic processes and statistical mechanics

Abstract

Some sufficient conditions are found for the distribution of the Ornstein–Uhlenbeck process with Lévy noise to be absolutely continuous or to have a smooth density. These conditions are necessary for one-dimensional processes with a nondegenerate drift coefficient. We also give a multidimensional analog of the condition that the drift parameter is nondegenerate.

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2003Financial Modelling with Jump Processes 1991Malliavin calculus for processes with jumps 1996On the existence of smooth densities for jump processes 1983Calcul des variations stochastique et processus de sauts 2006Malliavin calculus on the Wiener–Poisson space and its application to canonical SDE with jumps 2008Densities for Ornstein-Uhlenbeck processes with jumps 2006On the absolute continuity of Lévy processes with drift 2011ON THE SMOOTHNESS OF PDF OF SOLUTIONS TO SDE OF JUMP TYPE

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2011Exact Asymptotic for Distribution Densities of Lévy Functionals 2010On the absolute continuity of multidimensional Ornstein-Uhlenbeck processes

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