Thorin Classes of Lévy Processes and Their Transforms
نویسنده
چکیده
Thorin classes T (R+),κ > 0, of infinitely divisible distributions on R+ are defined and characterized. Poisson, Karlin and Bessel transforms of Thorin classes are investigated. The extended Thorin classes T (κ)(Rd), κ > 0, are also considered. Canonical representation and selfdecomposability properties of the Thorin subordinated Gaussian Lévy processes are discussed. As an example, the subordinated Cauchy process is considered in detail.
منابع مشابه
Lévy copulas: dynamics and transforms of Upsilon-type
Lévy processes and infinitely divisible distributions are increasingly defined in terms of their Lévy measure. In order to describe the dependence structure of a multivariate Lévy measure, Tankov (2003) introduced positive Lévy copulas. Together with the marginal Lévy measures they completely describe multivariate Lévy measures on R+ . In this paper, we show that any such Lévy copula defines it...
متن کاملLévy processes and Fourier multipliers
We study Fourier multipliers which result from modulating jumps of Lévy processes. Using the theory of martingale transforms we prove that these operators are bounded in Lp(Rd) for 1 < p < ∞ and we obtain the same explicit bound for their norm as the one known for the second order Riesz transforms.
متن کاملMartingale Transform and Lévy Processes on Lie Groups
This paper constructs a class of martingale transforms based on Lévy processes on Lie groups. From these, a natural class of bounded linear operators on the Lp-spaces of the group (with respect to Haar measure) for 1 < p < ∞, are derived. On compact groups these operators yield Fourier multipliers (in the Peter-Weyl sense) which include the second order Riesz transforms, imaginary powers of the...
متن کاملTwo kinds of conditionings for stable Lévy processes
Two kinds of conditionings for one-dimensional stable Lévy processes are discussed via h-transforms of excursion measures: One is to stay positive, and the other is to avoid the origin.
متن کاملWiener-Hopf factorization for Lévy processes having negative jumps with rational transforms
We give the closed form of the ruin probability for a Lévy processes, possibly killed at a constant rate, with completely arbitrary positive distributed jumps, and finite intensity negative jumps with distribution characterized by having a rational Laplace or Fourier transform. Abbreviated Title: WH-factors of Lévy processes with rational jumps.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007