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Exponential Functionals of Lévy Processes with Jumps
Am. J. Probab. Math. Stat
We study the exponential functional ∫ ∞ 0 e −ξs− dη s of two one-dimensional independent Lévy processes ξ and η, where η is a subordinator. In particular, we derive an integro-differential equation for the density of the exponential functional whenever it exists. Further, we consider the mapping Φ ξ for a fixed Lévy process ξ, which maps the law of η 1 to the law of the corresponding exponential functional ∫ ∞ 0 e −ξs− dη s , and study the behaviour of the range of Φ ξ for varyingfatcat:wotz5ecktjanrj26dczjwca4nm