On the range of exponential functionals of Lévy processes

2014/02/26 by Anita Behme, Alexander Lindner, Behme, Anita +3
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60E07 #60G10 #60G51 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1402.6559

openalex publication_date 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the support of the law of the exponential functional ∫₀^∞ e^-ξ_s- dη_s of two one-dimensional independent Lévy processes ξ and η. Further, we study the range of the mapping Φ_ξ for a fixed Lévy process ξ, which maps the law of η₁ to the law of the corresponding exponential functional ∫₀^∞ e^-ξ_s- dη_s. It is shown that the range of this mapping is closed under weak convergence and in the special case of positive distributions several characterizations of laws in the range are given.

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