<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Esquível, M.L.</style></author><author><style face="normal" font="default" size="100%">Krasii, NP</style></author><author><style face="normal" font="default" size="100%">Mota, P.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Auto and Externally Induced Regime Switching Diffusions</style></title><secondary-title><style face="normal" font="default" size="100%">Communications On Stochastic Analysis</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://serialsjournals.com/index.php?route=product/product/volumearticle&amp;issue_id=578&amp;product_id=304</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">14</style></volume><pages><style face="normal" font="default" size="100%">27-47</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In the current literature we can find mainly two approaches to the&lt;br /&gt;
SDE regime switching modeling. The traditional one, the externally induced&lt;br /&gt;
regime switching diffusions is described by the switching being derived from&lt;br /&gt;
a separate continuous time Markov process, with a finite, or denumerable,&lt;br /&gt;
state space { indexing the regimes { the random times of the regime switches&lt;br /&gt;
being exactly the jump times of the finite valued Markov process. There is a&lt;br /&gt;
first alternative approach in which the regime switching occurs whenever the&lt;br /&gt;
trajectory enters in some prescribed region on the state space; the regions we&lt;br /&gt;
consider will be mainly open intervals defined by unknown thresholds for the&lt;br /&gt;
trajectories; thresholds that, in principle, should also be estimated. In this&lt;br /&gt;
approach the partitioning of the the state space is already defined in the drift&lt;br /&gt;
and volatility of the SDE. In a second alternative approach the switching occurs&lt;br /&gt;
in a random way but at some random times defined when the trajectories hit&lt;br /&gt;
some prescribed thresholds, that again, must be estimated. We may designate&lt;br /&gt;
these two alternative approaches as auto-induced regime switching diffusions&lt;br /&gt;
as there is no external noise source to force the switching occurrence. We prove&lt;br /&gt;
a generalization of an existence result of the existence of auto-induced regime&lt;br /&gt;
switching SDE solutions for irregular coefficients and a result that encompasses&lt;br /&gt;
some of the cases of both externally and auto-induced regime switching SDE&lt;br /&gt;
solutions.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1-2</style></issue></record></records></xml>