Asymptotic results for exponential functionals of Levy processes
84 citations recorded by the source corpus.
In this work we give a complete description to the asymptotic behaviors of exponential functionals of L\'evy processes and divide them into five different types according to their convergence rates. Not only their exact convergence speeds are proved, the accurate limit constants are also given. As an application, we study the survival probabilities of continuous-state branching processes in random environment defined in He et al. (2016). Like the discrete case and branching diffusion in random environment, we classify them into five different types according to their extinction speeds.
Subfields: Finance, Management Science and Operations Research, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/20480dd62c6b57708abf7b194cd41a5624817015
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In Finance
In Management Science and Operations Research
In Mathematical Physics
Citations in the corpus
- Bernstein-gamma functions and exponential functionals of Levy Processes (2016, background): “However, in [45, 51] some very stringent restrictions are imposed on f .”
- Some Properties of the Kilbas-Saigo Function (2020, unknown): “SIMON random variable G1−t = logL1−t is the marginal at time t of a real Lévy process, since E[eizG1−t ] = Γ(1 + iz)t = etψ(z) for every z ∈ R, with ψ(z) = −γiz + ∫ 0 −∞ (e − 1− izx) dx |x|(e|x| − 1) · This is actually well-known - see Example E in [5].”