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There exist only a few known examples of subordinators for which thetransition probability density can be computed explicitly along side anexpression for its L\'evy measure and Laplace exponent. Such examples areuseful in several areas of applied probability, for example, they are used inmathematical finance for modeling stochastic time change, they appear incombinatorial probability to construct sampling formulae, which in turn isrelated to a variety of issues in the theory of coalescence models, moreover,they have also been extensively used in the potential analysis of subordinatedBrownian motion in dimension greater than or equal to 2. In this paper, we showthat Kendall's classic identity for spectrally negative L\'evy processes can beused to construct new families of subordinators with explicit transitionprobability semigroups. We describe the properties of these new subordinatorsand emphasise some interesting connections with explicit and previously unknownLaplace transform identities and with complete monotonicity properties ofcertain special functions.

New families of subordinators with explicit transition probability semigroup