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

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.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6173 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm