Probabilistic-statistical models

Spectral representations of stochastic processes in Banach spaces over infinite non-archimedean normed fields

S. V. Lyudkovskii

Moscow Institute of Radio-Engineering, Electronics and Automation

Abstract: The article is devoted to spectral representations of stochastic processes with values in Banach spaces over infinite fields $\bf K$ of zero characteristic with non-trivial non-archimedean norms. Different types of stochastic processes controlled by vector valued measures and their stochastic integrals are investigated. Theorems about spectral representations of such stochastic processes are proved.

Keywords: stochastic process, non-archimedean field, zero characteristic, random process, linear space, Banach space, stochastic integral, spectral representation.

UDC: 519.216.2, 512.625.5, 517.986

Received: 16.07.2011
Revised: 25.07.2011

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