<?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%">MELIKE SIRLANCI</style></author><author><style face="normal" font="default" size="100%">SUSAN E. LUCZAK</style></author><author><style face="normal" font="default" size="100%">I.G. ROSEN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ESTIMATION OF THE DISTRIBUTION OF RANDOM PARAMETERS IN DISCRETE TIME ABSTRACT PARABOLIC SYSTEMS WITH UNBOUNDED INPUT AND OUTPUT: APPROXIMATION AND CONVERGENCE</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">abstract parabolic systems</style></keyword><keyword><style  face="normal" font="default" size="100%">distributed parameter systems</style></keyword><keyword><style  face="normal" font="default" size="100%">distribution estimation</style></keyword><keyword><style  face="normal" font="default" size="100%">random parameters</style></keyword><keyword><style  face="normal" font="default" size="100%">regularly dissipative operators</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/en/articles/23/2/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">23</style></volume><pages><style face="normal" font="default" size="100%">44</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;A finite dimensional abstract approximation and convergence&amp;nbsp;theory is developed for estimation of the distribution of random parameters&amp;nbsp;in infinite dimensional discrete time linear systems with dynamics described&amp;nbsp;by regularly dissipative operators and involving, in general, unbounded input&amp;nbsp;and output operators. By taking expectations, the system is re-cast as an&amp;nbsp;equivalent abstract parabolic system in a Gelfand triple of Bochner spaces&amp;nbsp;wherein the random parameters become new space-like variables. Estimating&amp;nbsp;their distribution is now analogous to estimating a spatially varying coefficient&amp;nbsp;in a standard deterministic parabolic system. The estimation problems&amp;nbsp;are approximated by a sequence of finite dimensional problems. Convergence&amp;nbsp;is established using a state space-varying version of the Trotter-Kato semigroup&amp;nbsp;approximation theorem. Numerical results for a number of examples&amp;nbsp;involving the estimation of exponential families of densities for random parameters&amp;nbsp;in a diffusion equation with boundary input and output are presented&amp;nbsp;and discussed.&lt;/p&gt;
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