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

  • O. F. Casas-Sánchez Univ. Pedagógica y Tecnológica Colombia, Tunja, Colombia
  • J. Galeano-Peñaloza Dep. Mat., Univ. Nac. Colombia, Bogotá D.C., Colombia
  • J. J. Rodríguez-Vega Dep. Mat., Univ. Nac. Colombia, Bogotá D.C., Colombia
Keywords: Random walks, ultradiffusion, p-adic numbers, non-archimedean analysis

Abstract

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 associated to this operator. We also study the first passage time problem associated to $H^{\alpha}$ for $r<0.$



 

Author Biography

O. F. Casas-Sánchez, Univ. Pedagógica y Tecnológica Colombia, Tunja, Colombia



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Published
20.07.2021
How to Cite
Casas-Sánchez, O. F., J. Galeano-Peñaloza, and J. J. Rodríguez-Vega. “$p$-Adic Markov Process and the Problem of the First Return over Balls”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 7, July 2021, pp. 902 -12, doi:10.37863/umzh.v73i7.464.
Section
Research articles