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We propose an explicit construction of a stationary solution for a stochasticrecursion of the form $X\circ\theta=\phi(X)$ on a partially-ordered Polishspace, when the monotonicity of $\phi$ is not assumed. Under certainconditions, we show that an extension of the original probability space exists,on which a solution is well-defined, and construct explicitly this extension.We then provide conditions for the solution to be defined as well on theoriginal space. We finally apply these results to the stability study of twonon-monotonic queueing systems.

A generalized backwards scheme for solving non monotonic stochastic recursions