We obtain the large deviation principles for multidimensional first compound renewal processes Z(t) in the phase space R d , for this we find and investigate the rate function DZ (α). Also we find asymptotics for the Laplace transform of this process when the time goes to infinity, for this we find and investigate the so-called fundamental function AZ (µ).
We obtain the large deviation principles for multidimensional second compound renewal processes Y(t) in the phase space R d , for this we find and investigate the rate function DY (α). Also we find asymptotics for the Laplace transform of this process when the time goes to infinity, for this we find and investigate the so-called fundamental function AY (µ).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.