L{\'e}vy processes: concentration function and heat kernel bounds

28 Jun 2019  ·  Grzywny Tomasz, Szczypkowski Karol ·

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. read more

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Probability