Hilbert space representations of general discrete time stochastic processes

Dudley Paul Johnson

Stochastic Processes and their Applications, 1985, vol. 19, issue 1, 183-187

Abstract: We show that under mild conditions the joint densities Px1,...,xn) of the general discrete time stochastic process Xn on can be computed via Px1,...,xn(x1,...,xn) = ||[phi]T(x1)...T(xn)||2 where [phi] is in a Hilbert space , and T (x), x [epsilon] are linear operators on . We then show how the Central Limit Theorem can easily be derived from such representations.

Keywords: Hilbert; space; representation; central; limit; theorem; discrete; time; process (search for similar items in EconPapers)
Date: 1985
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