308 research outputs found
Selfdecomposability of Weak Variance Generalised Gamma Convolutions
Weak variance generalised gamma convolution processes are multivariate
Brownian motions weakly subordinated by multivariate Thorin subordinators.
Within this class, we extend a result from strong to weak subordination that a
driftless Brownian motion gives rise to a self-decomposable process. Under
moment conditions on the underlying Thorin measure, we show that this condition
is also necessary. We apply our results to some prominent processes such as the
weak variance alpha-gamma process, and illustrate the necessity of our moment
conditions in some cases
Differential Subordinations Involving Generalized Bessel Functions
In this paper our aim is to present some subordination and superordination
results, by using an operator, which involves the normalized form of the
generalized Bessel functions of first kind. These results are obtained by
investigating some appropriate classes of admissible functions. We obtain also
some sandwich-type results and we point out various known or new special cases
of our main results.Comment: 15 pages, accepted in Bulletin of the Malaysian Mathematical Sciences
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