Stochastic processes on non-Archimedean spaces with values in non-Archimedean fields

Abstract

Stochastic processes on topological vector spaces over non-Archimedean fields and with transition measures having values in non-Archimedean fields are defined and investigated. For this the non-Archimedean analog of the Kolmogorov theorem is proved. The analogos of Markov and Poisson processes are studied. For Poisson processes the corresponding Poisson measures are considered and the non-Archimedean analog of the Lèvy theorem is proved. Wide classes of stochastic processes are constructed.

34 pages

References in corpus (1)

• Integration by parts formulae for degenerate diffusion measures on path spaces and diffeomorphism groups

Cited by in corpus (5)

• Phase transitions for $P$-adic Potts model on the Cayley tree of order three
• $p$-adic discrete dynamical systems and their applications in physics and cognitive sciences
• Algebras of non-Archimedean measures on groups
• A note on q-Bernoulli numbers and polynomials
• Non-Archimedean stochastic processes on non-Archimedean manifolds