Bivariate Bernstein–gamma functions and moments of exponential functionals of subordinators

In this paper, we extend recent work on the class of Bernstein–gamma functions to bivariate functions. more general setting, determine Stirling-type asymptotic bounds which generalise, improve upon, and streamline those found for univariate Then, demonstrate importance power these results through an application exponential functionals Lévy processes. For a subordinator (a non-decreasing process) (Xs)s≥0, study its functional, ∫0te−Xsds, evaluated at finite, deterministic time t>0. Our main result here is explicit infinite convolution formula Mellin transform (complex moments) functional up t shown be equivalent series under very minor restrictions. Since subordinators are part universal factorisation concerning all processes believe that may turn out step towards in-depth finite horizon.