Families of ν-similar birth-death processes and limiting conditional distributions

Anna Poskrobko, Ewa Girejko
2015 Advances in Difference Equations  
We study, for a given process X , the conditions under which ν-similarity is provided, relations between similarity and ν-similarity of processes, and we analyze (doubly) limiting conditional distributions. We present sufficient conditions for the existence of at least one ν-similar process to a given one. Moreover, recursive formulas for birth and death rates of ν-similar processes are formulated. We apply differential equations and uniqueness of solutions to such equations to derive the main
more » ... esults of the paper. Finally, an example illustrates the applications of our results. MSC: Primary 60J80; 42C05; secondary 60J85
doi:10.1186/s13662-015-0588-2 fatcat:mku6w7w3a5ax3ni45prw6nmfwq