TY - JOUR
AU - Osypchuk, M.M.
PY - 2023/10/19
Y2 - 2024/05/18
TI - Bilateral estimates of some pseudo-derivatives of the transition probability density of an isotropic $\alpha$-stable stochastic process
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 15
IS - 2
SE - Scientific articles
DO - 10.15330/cmp.15.2.381-387
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/6521
SP - 381-387
AB - <p>In the paper, the transition probability density of an isotropic $\alpha$-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 $|\lambda|^\varkappa$ and $\lambda|\lambda|^{\varkappa-1}$, 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.</p>
ER -