Equivalences are established between common conditions on the characteristic exponent and the time behavior of the density supremum for vaguely continuous convolution semigroups on R^d, together with qualitative lower estimates under mild assumptions.
Asymptotic behaviour and estimates of slowly varying convolution semigroups
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abstract
We prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on $\mathbb{R} ^d$ under the assumption that its L\'{e}vy--Khintchine exponent varies slowly. We also derive some new estimates of the transition densities and Green functions.
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2019 1verdicts
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L{\'e}vy processes: concentration function and heat kernel bounds
Equivalences are established between common conditions on the characteristic exponent and the time behavior of the density supremum for vaguely continuous convolution semigroups on R^d, together with qualitative lower estimates under mild assumptions.