Weak Solutions of stochastic recursions: an explicit construction

Abstract

We propose an explicit construction of the solution of a stationary stochastic recursion of the form $X\circ \theta =\varphi (X)$ on a semi-ordered Polish space, when the monotonicity of $\varphi$ is not assumed. This solution exists on an enriched probability space (it is said \emph{weak}), provided the recursion is lattice-valued, and dominated by a proper monotonic stochastic recursion.

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