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We study a random map $T$ which consists of intermittent maps$\{T_{k}\}_{k=1}^{K}$ and a position dependent probability distribution$\{p_{k,\varepsilon}(x)\}_{k=1}^{K}$. We prove existence of a unique absolutelycontinuous invariant measure (ACIM) for the random map $T$. Moreover, we showthat, as $\varepsilon$ goes to zero, the invariant density of the random system$T$ converges in the $L^{1}$-norm to the invariant density of the deterministicintermittent map $T_{1}$. The outcome of this paper contains a first result onstochastic stability, in the strong sense, of intermittent maps.

A.C.I.M for Random Intermittent Maps : Existence, Uniqueness and Stochastic Stability