Weak Solutions of stochastic recursions: an explicit construction

We propose an explicit construction of the solution of a stationary stochastic recursion of the form $X\circθ=ϕ(X)$ on a semi-ordered Polish space, when the monotonicity of $ϕ$ 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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