An L2 convergence theorem for random affine mappings
- 1 March 1995
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 32 (1) , 183-192
- https://doi.org/10.2307/3214928
Abstract
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.Keywords
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