On Wiener-Hopf factors for stable processes

TL;DR

This paper provides a series representation for the logarithm of the bivariate Laplace exponent of alpha-stable processes, enhancing understanding of their probabilistic structure.

Contribution

It introduces a novel series representation for the logarithm of the Laplace exponent of alpha-stable processes, applicable to almost all alpha in (0,2].

Findings

Series representation for the logarithm of the Laplace exponent.

Applicable to almost all alpha in (0,2].

Improves analytical tools for stable processes.

Abstract

We give a series representation of the logarithm of the bivariate Laplace exponent $\kappa$ of $\alpha$-stable processes for almost all $\alpha \in (0,2]$.