2014/02/05 by James Burridge, Burridge, James, Mateusz Kwaśnicki +5
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1402.1062
openalex publication_date 2014/02/05 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28
There exist only a few known examples of subordinators for which the\ntransition probability density can be computed explicitly along side an\nexpression for its L 'evy measure and Laplace exponent. Such examples are\nuseful in several areas of applied probability, for example, they are used in\nmathematical finance for modeling stochastic time change, they appear in\ncombinatorial probability to construct sampling formulae, which in turn is\nrelated to a variety of issues in the theory of coalescence models, moreover,\nthey have also been extensively used in the potential analysis of subordinated\nBrownian motion in dimension greater than or equal to 2. In this paper, we show\nthat Kendall's classic identity for spectrally negative L 'evy processes can be\nused to construct new families of subordinators with explicit transition\nprobability semigroups. We describe the properties of these new subordinators\nand emphasise some interesting connections with explicit and previously unknown\nLaplace transform identities and with complete monotonicity properties of\ncertain special functions.\n