scholarly journals Equivalence betweenp-cyclic quasimonotonicity andp-cyclic monotonicity of affine maps

Optimization ◽  
2014 ◽  
Vol 64 (7) ◽  
pp. 1487-1497
Author(s):  
Eladio Ocaña ◽  
John Cotrina ◽  
Orestes Bueno
Keyword(s):  
Affine Maps ◽  
Cyclic Monotonicity

scholarly journals Ergodic affine maps of locally compact groups

1985 ◽  
Vol 37 (3) ◽  
pp. 363-372 ◽  
Author(s):  
Masahito DATEYAMA ◽  
Tatsuro KASUGA
Keyword(s):  
Locally Compact Groups ◽  
Compact Groups ◽  
Locally Compact ◽  
Affine Maps

The quasi-affine maps and fractals

1997 ◽  
Vol 2 (1) ◽  
pp. 9-12
Author(s):  
Lunhai Long ◽  
Gang Chen
Keyword(s):  
Affine Maps

An L 2 convergence theorem for random affine mappings

1995 ◽  
Vol 32 (01) ◽  
pp. 183-192 ◽  
Author(s):  
Robert M. Burton ◽  
Uwe Rösler
Keyword(s):  
Hilbert Space ◽  
Lyapunov Exponent ◽  
Bilinear Form ◽  
Convergence Theorem ◽  
Convergence In Distribution ◽  
Wasserstein Metric ◽  
Affine Mappings ◽  
Affine Maps ◽  
Second Moments ◽  
Contraction Condition

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.

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