Stochastic processes and their spectral representations over non-archimedean fields

S. V. Ludkovsky

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arXiv · 0801.1209

Stochastic processes and their spectral representations over non-archimedean fields

S. V. Ludkovsky

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Abstract

The article is devoted to stochastic processes with values in finite- and infinite-dimensional vector spaces over infinite fields $\bf K$ of zero characteristics with non-trivial non-archimedean norms. For different types of stochastic processes controlled by measures with values in $\bf K$ and in complete topological vector spaces over $\bf K$ stochastic integrals are investigated. Vector valued measures and integrals in spaces over $\bf K$ are studied. Theorems about spectral decompositions of non-archimedean stochastic processes are proved.

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S. V. Ludkovsky. 2008-01-08. Stochastic processes and their spectral representations over non-archimedean fields. https://arxiv.org/abs/0801.1209

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