Radonification of a cylindrical Lévy process-Reference-Cited by-同舟云学术

Radonification of a cylindrical Lévy process

Published:2023-05-16 Issue:2 Volume:31 Page:199-204
ISSN:0926-6364
Container-title:Random Operators and Stochastic Equations
language:en
Short-container-title:

Author:

Alvarado-Solano Anddy E.¹

Affiliation:

1. Escuela de Matemática , Instituto Tecnológico de Costa Rica , Cartago 159-7050 , Costa Rica

Abstract

Abstract In this work, we present a direct proof about radonification of a cylindrical Lévy process. The radonification technique has been very useful to define a genuine stochastic process starting from a cylindrical process; this is possible thanks to the Hilbert–Schmidt operators. With this work, we want to propose a self-contained simple proof to those who are not familiar with this method and also present our result which is to apply the radonification method to the case of a cylindrical Lévy process.

Publisher

Walter de Gruyter GmbH

Subject

Statistics and Probability,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rose-2023-2010/pdf

Reference10 articles.

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3. D. Applebaum, Lévy Processes and Stochastic Calculus, 2nd ed., Cambridge Stud. Adv. Math. 116, Cambridge University, Cambridge, 2009.

4. D. Applebaum and M. Riedle, Cylindrical Lévy processes in Banach spaces, Proc. Lond. Math. Soc. (3) 101 (2010), no. 3, 697–726.

5. C. A. Fonseca-Mora, Existence of continuous and Càdlàg versions for cylindrical processes in the dual of a nuclear space, J. Theoret. Probab. 31 (2018), no. 2, 867–894.