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arXiv · 2305.12790

Bilateral estimates of some pseudo-derivatives of the transition probability density of an isotropic $α$-stable stochastic process

Mykhailo Osypchuk
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Abstract

In the paper, the transition probability density of isotropic $α$-stable stochastic process in a finite dimensional Euclidean space is considered. The results of applying pseudo differential operators with respect spatial variables to this function are estimated from the both side: above and below. Operators in the consideration are defined by the symbols $|λ|^\varkappa$ and $λ|λ|^{\varkappa-1}$, where $\varkappa$ is some constant. The first operator with negative sign is fractional Laplacian and the second one multiplied by imaginary unit is fractional gradient.

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Mykhailo Osypchuk. 2023-05-22. Bilateral estimates of some pseudo-derivatives of the transition probability density of an isotropic $α$-stable stochastic process. https://doi.org/10.15330/cmp.15.2.381-387

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