Jan Rosinski
Mathematics/UTK

PREPRINTS:


Inverse problems for regular variation of linear filters, a cancellation property for sigma-finite measures, and identification of stable laws (with Martin Jacobsen, Thomas Mikosch, and Gennady Samorodnitsky)

ABSTRACT. We study a group of related problems: the extent to which the presence of regular variation in the tail of certain sigma-finite measures at the output of a linear filter determines the corresponding regular variation of a measure at the input to the filter. This turns out to be related to the presence of a particular cancellation property in sigma-finite measures, which, in turn, is related to the uniqueness of the solution of certain functional equations. The techniques we develop are applied to weighted sums of iid random variables, to products of independent random variables, and to stochastic integrals with respect to Levy motions.
(To appear in the Annals of Applied Probability.)

General Upsilon-transformations (with Ole Barndorff-Nielsen and Steen Thorbjornsen)

ABSTRACT. In this paper we introduce a general class of transformations of (all or most of) the class of d-dimensional Levy measures on Rd, into itself. We refer to transformations of this type as Upsilon-transformations. Closely associated to these are mappings of the set of all infinitely divisible laws on Rd into itself. In considerable generality, the mappings are one-to-one, regularising and bi-continuous. Furthermore, in many cases the transformations have a stochastic interpretation in terms of stochastic integrals with respect to Levy processes.
(To appear in the ALEA - Latin American Journal Of Probability And Mathematical Statistics.)

On the marginal effects of variables in the log-transformed sample selection models (with Steven T. Yen).

ABSTRACT. We derive the conditional mean of the limited dependent variable for a general class of sample selection models with a logarithmically transformed dependent variable. An application to household charity donation suggests use of the correct conditional mean is important.
(In press, Economics Letters, doi:10.1016/j.econlet.2007.10.019 )

Simulation of Levy processes

ABSTRACT. Simulation methods of Levy processes based on random walk approximation, series representations of Levy processes, and on Poisson and Gaussian approximations are reviewed. Formulae for simulation of some Levy processes are given as examples.
(To appear in Encyclopedia of Statistics in Quality and Reliability: Computationally Intensive Methods and Simulation, Wiley 2008.)

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Last Modified: February, 2008.