LEVY PROCESSES WITH RESPECT TO THE WHITTAKER CONVOLUTION

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Sousa, R (Author) Other; Guerra, M (Author) Other; Yakubovich, SB (Author) FCUP

Journal

Title: Transactions of the American Mathematical Society

Vol. 374

Pages: 2383-2419

ISSN: 0002-9947

Publisher: American Mathematical Society

Indexing

ISI Web of Knowledge - 7 Citations

Scopus - 8 Citations

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 37