Time--space harmonic polynomials relative to a L\'{e}vy process

TL;DR

This paper derives explicit formulas and recurrence relations for time-space harmonic polynomials associated with Lévy processes, and explores their connection to Kailath–Segall orthogonal polynomials.

Contribution

It provides the first closed-form expressions and recurrence relations for these polynomials, linking them to orthogonal polynomial families.

Findings

Closed-form expressions for harmonic polynomials

Recurrence relations established

Connection to Kailath–Segall orthogonal polynomials

Abstract

In this work, we give a closed form and a recurrence relation for a family of time--space harmonic polynomials relative to a L\'{e}vy process. We also state the relationship with the Kailath--Segall (orthogonal) polynomials associated to the process.