Stochastic Perturbations and Invariant Measures of Position Dependent Random Maps via Fourier Approximations
2015 ◽
Vol 25
(09)
◽
pp. 1550112
Keyword(s):
Let T = {τ1(x), τ2(x),…, τK(x); p1(x), p2(x),…, pK(x)} be a position dependent random map which possesses a unique absolutely continuous invariant measure [Formula: see text] with probability density function [Formula: see text]. We consider a family {TN}N≥1 of stochastic perturbations TN of the random map T. Each TN is a Markov process with the transition density [Formula: see text], where qN(x, ⋅) is a doubly stochastic periodic and separable kernel. Using Fourier approximation, we construct a finite dimensional approximation PN to a perturbed Perron–Frobenius operator. Let [Formula: see text] be a fixed point of PN. We show that [Formula: see text] converges in L1 to [Formula: see text].
2011 ◽
Vol 21
(01)
◽
pp. 113-123
◽
2001 ◽
2000 ◽
Vol 73
(5)
◽
pp. 439-456
◽
Keyword(s):
2020 ◽
Vol 20
(1)
◽
pp. 109-120
◽
1987 ◽
Vol 48
(178)
◽
pp. 565-565
◽
1992 ◽
Vol 114
(4)
◽
pp. 580-587
◽