P-adic Markov process and the problem of the first return over balls
Let $\langle x\rangle^α=(\max\{|x|_{p},p^r\})^α$ and $H^αφ=\mathcal{F}^{-1}[(\langle ξ\rangle^α -p^{rα})\mathcal{F}φ]$, in this article we study the Markov process associated to this operator and the first passage time problem associated to $H^α$.
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