LEVY PROCESSES WITH RESPECT TO THE WHITTAKER CONVOLUTION

• Tipo: Artigo em Revista Científica Internacional
• Data: 2021

Autores

Sousa, R (Autor) Outra; Guerra, M (Autor) Outra; Yakubovich, SB (Autor) FCUP

Revista

Título: Transactions of the American Mathematical Society

Vol. 374

Páginas: 2383-2419

ISSN: 0002-9947

Editora: American Mathematical Society

Indexação

ISI Web of Knowledge - 7 Citações

Scopus - 8 Citações

Outras Informações

ID Authenticus: P-00T-KZ2

DOI: 10.1090/tran/8294

Abstract (EN): It is natural to ask whether it is possible to construct Levy-like processes where actions by random elements of a given semigroup play the role of increments. Such semigroups induce a convolution-like algebra structure in the space of finite measures. In this paper, we show that the Whittaker convolution operator, related with the Shiryaev process, gives rise to a convolution measure algebra having the property that the convolution of probability measures is a probability measure. We then introduce the class of Levy processes with respect to the Whittaker convolution and study their basic properties. We obtain a martingale characterization of the Shiryaev process analogous to Levy's characterization of Brownian motion. Our results demonstrate that a nice theory of Levy processes with respect to generalized convolutions can be developed for differential operators whose associated convolution does not satisfy the usual compactness assumption on the support of the convolution.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 37