The Entrance Law of the Excursion Measure of the Reflected Process for Some Classes of Lévy Processes
We provide integral formulae for the Laplace transform of the entrance law of the reflected excursions for symmetric Lévy processes in terms of their characteristic exponent. For subordinate Brownian motions and stable processes we express the density of the entrance law in terms of the generalized...
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| Veröffentlicht in: | Acta applicandae mathematicae 2020-10, Vol.169 (1), p.59-77 |
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| creator | Chaumont, Loïc Małecki, Jacek |
| description | We provide integral formulae for the Laplace transform of the entrance law of the reflected excursions for symmetric Lévy processes in terms of their characteristic exponent. For subordinate Brownian motions and stable processes we express the density of the entrance law in terms of the generalized eigenfunctions for the semigroup of the process killed when exiting the positive half-line. We use the formulae to study in-depth properties of the density of the entrance law such as asymptotic behavior of its derivatives in time variable. |
| doi_str_mv | 10.1007/s10440-019-00288-8 |
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| subjects | Applications of Mathematics Asymptotic properties Calculus of Variations and Optimal Control Optimization Computational Mathematics and Numerical Analysis Density Eigenvectors Entrances Laplace transforms Mathematics Mathematics and Statistics Partial Differential Equations Probability Theory and Stochastic Processes |
| title | The Entrance Law of the Excursion Measure of the Reflected Process for Some Classes of Lévy Processes |
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