View source for Stochastic point process with limited memory

A [[Stochastic point process|stochastic point process]] defined by a sequence of random variables <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090180/s0901801.png" />,

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090180/s0901802.png" /></td> </tr></table>

in which the intervals <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090180/s0901803.png" /> are mutually-independent random variables. Such processes are closely related to renewal processes (see [[Renewal theory|Renewal theory]]), in which the <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090180/s0901804.png" /> (<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s090/s090180/s0901805.png" />) are independent identically-distributed random variables.