Work

Ornstein-Uhlenbeck processes driven by cylindrical Lévy processes

Year: 2012

Type: preprint

Abstract: In this article we introduce a theory of integration for deterministic, operator-valued integrands with respect to cylindrical Lévy processes in separable Banach spaces. Here, a cylindrical Lévy process is understood in the classical framework of cylindrical random variables and cylindrical measures, and thus, it can be considered as a natural generalisation of cylindrical Wiener processes or white noises. Depending on the underlying Banach space, we provide necessary and/or sufficient conditions for a function to be integrable. In the last part, the developed theory is applied to define Ornstein-Uhlenbeck processes driven by cylindrical Lévy processes and several examples are considered.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1212.3832

Author: Riedle, Markus

Institution: King's College London

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Award: G8404142816

OpenAlex ID: W2951871265

Cites: 23

Cited by: 2

Related to: 20