Distribution tails of a history-dependent random linear recursion

We consider a history-dependent random linear recursion, adapting a continuous-time framework introduced by Clifford and Stirzaker. Typically, the main object of interest in the study of history-dependent processes is the evolution and asymptotic behavior of their first and second moments. We apply the methodology developed by Clifford and Stirzaker to study the evolution of distribution tails of the process by utilizing a certain affinity between the asymptotic structure of the tails in a regular variation regime and a linear structure of moments in the class of models introduced by Clifford and Stirzaker.