Generalized L/'evy Stochastic Areas and Selfdecomposability

TL;DR

This paper explores the structure of generalized Lévy stochastic areas, revealing their connection to selfdecomposable distributions and providing new interpretations involving Bessel functions and van Dantzig class characteristic functions.

Contribution

It demonstrates that the conditional characteristic function of generalized Lévy stochastic areas can be expressed as a product of a selfdecomposable distribution and its background driving function, offering new insights.

Findings

Connection between stochastic areas and selfdecomposable distributions

Stochastic interpretation of Bessel function ratios

Examples from van Dantzig class characteristic functions

Abstract

We show that a conditional characteristic function of generalized L\'evy stochastic areas can be viewed as a product a selfdecomposable distribution (i.e., L\'evy class L distribution) and its background driving characteristic function. This provides a stochastic interpretation for a ratio of some Bessel functions as well as examples of characteristic functions from van Dantzig class.