INVARIANT MEASURES FOR RANDOM MAPS VIA INTERPOLATION
2013 ◽
Vol 23
(02)
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pp. 1350025
Keyword(s):
Let T = {τ1, τ2, …, τK; p1, p2, …, pK} be a position dependent random map on [0, 1], where {τ1, τ2, …, τK} is a collection of nonsingular maps on [0, 1] into [0, 1] and {p1, p2, …, pK} is a collection of position dependent probabilities on [0, 1]. We assume that the random map T has a unique absolutely continuous invariant measure μ with density f*. Based on interpolation, a piecewise linear approximation method for f* is developed and a proof of convergence of the piecewise linear method is presented. A numerical example for a position dependent random map is presented.
1987 ◽
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pp. 301-308
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