@article{Casas-Sánchez_Galeano-Peñaloza_Rodríguez-Vega_2021, title={$p$-Adic Markov process and the problem of the first return over balls}, volume={73}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/464}, DOI={10.37863/umzh.v73i7.464}, abstractNote={<p>UDC 511.225, 519.217, 511.225.1, 303.532</p> <p>We consider the pseudodifferential operator defined as $H^{\alpha}\varphi = \mathcal{F}^{-1}[(\langle \xi\rangle^{\alpha} - p^{r\alpha})\mathcal{F}_{\varphi}],$ where $ \langle \xi \rangle= (\max\{|\xi|_{p}, p^r\})^{\alpha}$ and study the Markov process associated to this operator. We also study the first passage time problem associated to $H^{\alpha}$ for $r&lt;0.$</p> <p><br><br></p> <p>&nbsp;</p&gt;}, number={7}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Casas-Sánchez, O. F. and Galeano-Peñaloza, J. and Rodríguez-Vega, J. J.}, year={2021}, month={Jul.}, pages={902 - 912} }