Question: Iterated random functions. Let E be a countable set, .F;F/ an arbitrary event space, f W E F ! E a measurable function, and .Ui

Iterated random functions. Let E be a countable set, .F;F/ an arbitrary event space, f W E F ! E a measurable function, and .Ui /i1 a sequence of i.i.d. random variables taking values in .F;F/. Let .Xn/n0 be recursively defined by X0 D x 2 E, and XnC1 D f .Xn; UnC1/ for n 0. Show that .Xn/n0 is a Markov chain and determine the transition matrix.

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