A note on the existence of transition probability densities of Lévy processes
By Viktorya Knopova, René L. Schilling. 2010
119 citations recorded by the source corpus.
Abstract. We prove necessary and sufficient conditions for the existence of (smooth) transition probability densities for Lévy processes and isotropic Lévy processes. Under some mild conditions on the characteristic exponent we calculate the asymptotic behaviour of the transition density as and and show a ratio-limit theorem.
Subfields: Finance, Management Science and Operations Research, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6f7135b739a2c57ae5ac7a418c8d96b25dde69bf
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Citations in the corpus
- Some theorems on Feller processes: transience, local times and ultracontractivity (2011, background): “the symbol p(x,ξ) is just the exponent ψ(ξ) of the characteristic function, cf. Section 2. Therefore, (1.4) is the Hartman–Wintner condition for the existence of smooth density functions, see [13] or [19] for a recent study; (1.5) is the classic Chung-Fuchs criterion for the transience of the proces”
- Gradient estimate for Ornstein–Uhlenbeck jump processes (2010, methodology): “rocess is pure jump, existence and regularities of the transition density have been derived by using conditions on the symbol ∗Supported in part by WIMCS, NNSFC(10721091). 1 or the L´evy measure (see [8, 9, 12] and references within); see also [5, 11] for heat kernel upper bounds for α-stable proces”