Bohr almost periodicity is equivalent to p-adic continuity as a path event for these processes, but the equivalence does not hold for Weyl or Besicovitch almost periodicity; the result extends to random fields.
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Almost periodicity as a path property for $p$-adic self-similar processes with stationary increments
Bohr almost periodicity is equivalent to p-adic continuity as a path event for these processes, but the equivalence does not hold for Weyl or Besicovitch almost periodicity; the result extends to random fields.