Published online by Cambridge University Press: 14 July 2016
We consider the composition of random i.i.d. affine maps of a Hilbert space to itself. We show convergence of the nth composition of these maps in the Wasserstein metric via a contraction argument. The contraction condition involves the operator norm of the expectation of a bilinear form. This is contrasted with the usual contraction condition of a negative Lyapunov exponent. Our condition is stronger and easier to check. In addition, our condition allows us to conclude convergence of second moments as well as convergence in distribution.
Supported in part by AFOSR Grant 91-0215 and NSF Grant DMS-9103738.
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