<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MD SHAFIQUL ISLAM</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">AN ALTERNATIVE ELEMENTARY METHOD FOR APPROXIMATION OF INVARIANT MEASURES FOR RANDOM MAPS</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">37A05</style></keyword><keyword><style  face="normal" font="default" size="100%">37E05</style></keyword><keyword><style  face="normal" font="default" size="100%">37H99</style></keyword><keyword><style  face="normal" font="default" size="100%">37M25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/26/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">26</style></volume><pages><style face="normal" font="default" size="100%">22</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we describe an alternative elementary method of approximating&amp;nbsp;invariant measures for random maps. Instead of computing Ulam’s matrices&amp;nbsp;associated with the Frobenious-Perron operator for random map we compute&amp;nbsp;matrices which approximate Ulam’s matrices.&lt;br /&gt;
Let $T = \{\tau_1(x), \tau_2(x), . . . , \tau_K(x); p_1, p_2, . . . , p_K\}$ be a random map which posses a&amp;nbsp;unique absolutely continuous invariant measure $\hat\mu$&amp;nbsp;with probability density function $\hat f$. With our elementary method it is possible to develop and implement algorithms&amp;nbsp;for the approximation of the invariant measure $\hat\mu$&amp;nbsp; with a given bound on the error&amp;nbsp;of the approximation. One of the main advantages of our method is that we do not&amp;nbsp;need to deal with the inverse of the component maps of the random maps. Our result&amp;nbsp;is a generalization of the result of Galatolo and Nisoli (see the paper [12] Galatolo,&amp;nbsp;S. and Nisoli, I, An elementary approch to rigorous approximation of Invariant&amp;nbsp;measures, &lt;em&gt;SIAM J. Appl. Dynamical Systems&lt;/em&gt;, &lt;strong&gt;13&lt;/strong&gt;, No. 2 (2014), 958-985) of&amp;nbsp;single piecewise&amp;nbsp; expanding maps to results of random maps. We present a numerical&amp;nbsp;example.&lt;/p&gt;
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