$p$-Adic Markov process and the problem of the first return over balls

• Date: 2021
• Main Authors: Casas-Sánchez, O. F., Galeano-Peñaloza, J., Rodríguez-Vega, J. J., Casas-Sánchez, Oscar, Galeano-Peñaloza, Jeanneth
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2021
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/464
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 511.225, 519.217, 511.225.1, 303.532 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 assoc...