$p$-Adic Markov process and the problem of the first return over balls - Casas-Sánchez, O. F.; Galeano-Peñaloza, J.; Rodríguez-Vega, J. J. (Ukrains’kyi Matematychnyi Zhurnal, 2021)
UDC 511.225, 519.217, 511.225.1, 303.532We 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