On Two Selected Topics Connected with Stochastic Systems Theory

Rozanov, Y.A. (1976). On Two Selected Topics Connected with Stochastic Systems Theory. IIASA Research Memorandum. IIASA, Laxenburg, Austria: RM-76-041

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Abstract

The existence and the explicit form of the minimal Markov process which contains as a component a given stationary process are established. It is shown in particular that the future/past splitting subspace of the multivariate stationary process is finite-dimensional if and only if the process has a rational spectral densities matrix.

The property of being stochastically continuous is obtained as the condition for continuation of the sigma-algebras associated with a process with independent increments which usually represents a stochastic disturbance of the system considered. This property gives us the left-side continuation of the sigma-algebras in the case of the arbitrary process in a metric space.

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