L{é}vy processes: concentration function and heat kernel bounds

Tomasz Grzywny; Karol Szczypkowski

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arXiv · 1907.00778

L{é}vy processes: concentration function and heat kernel bounds

Tomasz Grzywny·Karol Szczypkowski

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Abstract

We investigate densities of vaguely continuous convolution semigroups of probability measures on $\mathbb{R}^d$. We expose that many typical conditions on the characteristic exponent repeatedly used in the literature of the subject are equivalent to the behaviour of the maximum of the density as a function of time variable. We also prove qualitative lower estimates under mild assumptions on the corresponding jump measure and the characteristic exponent.

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Tomasz Grzywny, Karol Szczypkowski. 2019-06-28. L{é}vy processes: concentration function and heat kernel bounds. https://arxiv.org/abs/1907.00778

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