An L 2 convergence theorem for random affine mappings
1995 ◽
Vol 32
(01)
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pp. 183-192
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Keyword(s):
We consider the composition of random i.i.d. affine maps of a Hilbert space to itself. We show convergence of thenth 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.
2007 ◽
Vol 329
(2)
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pp. 759-765
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2010 ◽
Vol 14
(5)
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pp. 1881-1901
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1996 ◽
Vol 9
(2)
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pp. 263-283
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2017 ◽
Vol 2017
(1)
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Keyword(s):
2019 ◽
Vol 372
(4)
◽
pp. 2357-2388
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