A note on the existence of transition probability densities of Levy processes

作者：Knopova Victoria^*; Schilling Rene L

来源：Forum Mathematicum, 2013, 25(1): 125-149.

DOI：10.1515/FORM.2011.108

• Transition probability density
• absolute continuity
• Hartman-Wintner condition
• monotone rearrangement
• anisotropic Sobolev spaces
• volume doubling

We prove necessary and sufficient conditions for the existence of (smooth) transition probability densities for Levy processes and isotropic Levy processes. Under some mild conditions on the characteristic exponent we calculate the asymptotic behaviour of the transition density as t -> 0 and t -> infinity and show a ratio-limit theorem.

• 出版日期2013-1