Probabilistic-statistical models

Spectral functions of stochastic processes on infinite fields with non-archimedeval normalizations

S. V. Lyudkovskii

Moscow Institute of Radio-Engineering, Electronics and Automation

Abstract: The article is devoted to stochastic processes with values in finite- and infinite-dimensional vector spaces over infinite fields $\bf K$ of zero characteristic with non-trivial non-archimedean norms. Stochastic integrals are investigated for different types of stochastic processes controlled by measures with values in $\bf K$ and in complete topological vector spaces over the field $\bf K$. Spectral decompositions of non-archimedean stochastic processes are studied.

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

UDC: 519.216.2, 512.625.5, 517.986

Received: 17.06.2010
Revised: 27.06.2010

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