Work

Itô’s formula for Itô processes defined with respect to a cylindrical martingale-valued measure

Year: 2026

Type: article

Abstract: Using the authors’ recently developed stochastic integration [Stoch PDE: Anal Comp, 2024], we prove an Itô formula for Hilbert space-valued Itô processes defined with respect to a cylindrical martingale-valued measure. We develop some tools from stochastic analysis, as are the predictable and optional quadratic variation of a stochastic integral, the continuous and purely discontinuous parts of an integral process, and a Riemann representation formula. As an application of our Itô formula, we prove a Burkholder inequality for the stochastic integral defined with respect to a cylindrical martingale-valued measure. Finally, we derive Itô formulas for Hilbert space-valued martingale-valued measures and for cylindrical square integrable martingales.

Source: Stochastic Analysis and Applications

DOI: 10.1080/07362994.2026.2701258

Authors: S. Cambronero, David Campos, C. A. Fonseca-Mora, D. Mena

Institution: Universidad de Costa Rica

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funders: Universidad de Costa Rica, Vicerrectoría de Investigación, Universidad de Costa Rica

OpenAlex ID: W4406073883

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