scholarly journals Critically finite random maps of an interval

2020 ◽  
Vol 40 (8) ◽  
pp. 4839-4906
Author(s):  
Jason Atnip ◽  
◽  
Mariusz Urbański ◽  
Keyword(s):  
Random Maps

Phase transition in piecewise linear random maps in the interval

2021 ◽  
Vol 31 (9) ◽  
pp. 093112
Author(s):  
Cesar Maldonado ◽  
Ricardo A. Pérez Otero
Keyword(s):  
Phase Transition ◽  
Piecewise Linear ◽  
Random Maps

scholarly journals Deterministic representation for position dependent random maps

2008 ◽  
Vol 22 (3) ◽  
pp. 529-540 ◽  
Author(s):  
Wael Bahsoun ◽  
◽  
Christopher Bose ◽  
Anthony Quas ◽  
◽  
...  
Keyword(s):  
Random Maps

Quenched stochastic stability for eventually expanding-on-average random interval map cocycles

2018 ◽  
Vol 39 (10) ◽  
pp. 2769-2792
Author(s):  
GARY FROYLAND ◽  
CECILIA GONZÁLEZ-TOKMAN ◽  
RUA MURRAY
Keyword(s):  
Invariant Measures ◽  
Single Step ◽  
Absolutely Continuous ◽  
Random Maps ◽  
Driving Mechanisms ◽  
The Family ◽  
Ulam’S Method ◽  
Ulam's Method ◽  
Invariant Densities ◽  
Absolutely Continuous Invariant

The paper by Froyland, González-Tokman and Quas [Stability and approximation of random invariant densities for Lasota–Yorke map cocycles.Nonlinearity27(4) (2014), 647] established fibrewise stability of random absolutely continuous invariant measures (acims) for cocycles of random Lasota–Yorke maps under a variety of perturbations, including ‘Ulam’s method’, a popular numerical method for approximating acims. The expansivity requirements of Froylandet alwere that the cocycle (or powers of the cocycle) should be ‘expanding on average’ before applying a perturbation, such as Ulam’s method. In the present work, we make a significant theoretical and computational weakening of the expansivity hypotheses of Froylandet al, requiring only that the cocycle be eventually expanding on average, and importantly,allowing the perturbation to be applied after each single step of the cocycle. The family of random maps that generate our cocycle need not be close to a fixed map and our results can handle very general driving mechanisms. We provide a detailed numerical example of a random Lasota–Yorke map cocycle with expanding and contracting behaviour and illustrate the extra information carried by our fibred random acims, when compared to annealed acims or ‘physical’ random acims.

On the Convergence of Iterated Random Maps with Applications to the MCEM Algorithm

COMPSTAT ◽  
1998 ◽  
pp. 317-322
Author(s):  
G. Fort ◽  
E. Moulines ◽  
P. Soulier
Keyword(s):  
Random Maps ◽  
Mcem Algorithm

scholarly journals Random maps

2015 ◽  
Vol 51 ◽  
pp. 133-149
Author(s):  
Céline Abraham ◽  
Jérémie Bettinelli ◽  
Gwendal Collet ◽  
Igor Kortchemski
Keyword(s):  
Random Maps
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