On simulation from the marginal distribution of a Student t and generalized hyperbolic Lévy process

Note that several slightly different parameterizations are used, in particular 2ν instead of ν. It is well-known since [5] that this distribution is infinitely divisible, thus there is a Lévy process X such that X(1) ∼ Tν . While there is a simple elegant one-liner (Bailey’s method), see [2], to simulate from the distribution of X(1), ie Tν , it seems, that very little is known about simulating from the distribution of X(t) for non-integer t. We may want to denote that distribution by T ∗t ν , referring the corresponding convolution semigroup. Stochastic processes with Student mariginals have been studied recently in [7].