By using a symbolic technique known in the literature as the classical umbral calculus, we characterize two classes of polynomials related to Lévy processes: the Kailath-Segall and the time-space harmonic polynomials. We provide the Kailath-Segall formula in terms of cumulants and we recover simple closed-forms for several families of polynomials with respect to not centered Lévy processes, such as the Hermite polynomials with Brownian motion, Poisson-Charlier polynomials with Poisson processes, actuarial polynomials with Gamma processes, first kind Meixner polynomials with Pascal processes, and Bernoulli, Euler, and Krawtchuk polynomials with suitable random walks. © 2013 Copyright Taylor and Francis Group, LLC.

On some applications of a symbolic representation of non centered Lévy processes / Elvira Di, Nardo; Oliva, I.. - 42:21(2013), pp. 3974-3988. [10.1080/03610926.2011.642920]

On some applications of a symbolic representation of non centered Lévy processes

Oliva I.
2013

Abstract

By using a symbolic technique known in the literature as the classical umbral calculus, we characterize two classes of polynomials related to Lévy processes: the Kailath-Segall and the time-space harmonic polynomials. We provide the Kailath-Segall formula in terms of cumulants and we recover simple closed-forms for several families of polynomials with respect to not centered Lévy processes, such as the Hermite polynomials with Brownian motion, Poisson-Charlier polynomials with Poisson processes, actuarial polynomials with Gamma processes, first kind Meixner polynomials with Pascal processes, and Bernoulli, Euler, and Krawtchuk polynomials with suitable random walks. © 2013 Copyright Taylor and Francis Group, LLC.
2013
Cumulant; Kailath-Segall polynomial; Lévy process; Time-space harmonic polynomial; Umbral calculus
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On some applications of a symbolic representation of non centered Lévy processes / Elvira Di, Nardo; Oliva, I.. - 42:21(2013), pp. 3974-3988. [10.1080/03610926.2011.642920]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1285586
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