On the convergence of sequences of iterates of random-valued vector functions

Abstract

Abstract. Given a probability space (Ω, A, P ) and a subset X of a normed space we consider functions f : X ×

Weak limit of iterates of some random-valued functions and its application

“…1.4B]. The paper [6] by Rafa l Kapica brings theorems on the convergence a.s. and in L 1 of those sequences of iterates in the case where X is a closed subset of a Banach lattice. A simple criterion for the convergence in law of (f n (x, ·)) n∈N to a random variable independent of x ∈ X was proved in [1] and applied to the equation…”

On a Refinement Type Equation

“…This definition of iterates were introduced independently in [3] and [14], and then studied also in [1], [17] and [20]. It turns out that such iterates are useful for instance in solving functional equations (see [2], [16], [18]).…”

Weak law of large numbers for iterates of random-valued functions

“…1.4B]. The paper [4] by Rafa l Kapica brings theorems on the convergence a.s. and in L 1 of those sequences of iterates in the case where X is a closed subset of a Banach lattice. A simple criterion for the convergence in law of (f n (x, ·)) n∈N to a random variable independent of x ∈ X was proved in [1] and applied to the equation…”