<mods:mods version="3.3" xsi:schemaLocation="http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-3.xsd" xmlns:mods="http://www.loc.gov/mods/v3" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><mods:titleInfo><mods:title>One-dimensional semi-Markov evolutions with&#13;
general Erlang sojourn times</mods:title></mods:titleInfo><mods:name type="personal"><mods:namePart type="given">А. А.</mods:namePart><mods:namePart type="family">Pogoruі</mods:namePart><mods:role><mods:roleTerm type="text">author</mods:roleTerm></mods:role></mods:name><mods:name type="personal"><mods:namePart type="given">Ramón М.</mods:namePart><mods:namePart type="family">Rodríguez-Dagnіno</mods:namePart><mods:role><mods:roleTerm type="text">author</mods:roleTerm></mods:role></mods:name><mods:abstract>In this paper we study a one-dimensional random motion by having a general Erlang&#13;
distribution for the sojourn times and we obtain higher order hyperbolic equations for this case. We&#13;
apply the methodology of random evolutions to ¯nd the partial di®erential equations governing the&#13;
particle motion and we obtain a factorization of these equations. As a particular case we ¯nd the linear&#13;
biwave equation for the symmetric motion case and 2-Erlang distributions for the sojourn times of a&#13;
semi-Markov evolution.</mods:abstract><mods:classification authority="lcc">Mathematical Analysis</mods:classification><mods:originInfo><mods:dateIssued encoding="iso8061">2005</mods:dateIssued></mods:originInfo><mods:originInfo><mods:publisher>ROSE</mods:publisher></mods:originInfo><mods:genre>Article</mods:genre></mods:mods>