Math @ Duke

Publications [#10350] of Jonathan C. Mattingly
Papers Published
 Mattingly, J. C., Contractivity and ergodicity of the random map {$x\mapsto\vert x\theta\vert $},
Teor. Veroyatnost. i Primenen., vol. 47 no. 2
(2002),
pp. 388397 [MR2004f:60148], [pdf]
(last updated on 2004/07/13)
Author's Comments: Also in SIAM Journal: Theory Probab. Appl.
Abstract: The long time behavior of the random map $x_n
\mapsto
x_{n+1} x_n\theta_n$ is studied under
various assumptions
on the distribution of the $\theta_n$. One of the
interesting features of this random dynamical
system is that
for a single fixed deterministic $\theta$ the
map is not a
contraction, while the composition is almost
surely a
contraction if $\theta$ is picked randomly
with only mild
assumptions on the distribution of the
$\theta$'s. The
system is useful as an explicit model where
more abstract
ideas can be explored concretely. We explore
various
measures of convergence rates, hyperbolically
from
randomness, and the structure of the random
attractor.


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