Itô's formula for Lévy-Itô processes taking values in the dual of nuclear space

2026/08/06 by C. A. Fonseca-Mora
Mathematics · #math.PR #msc:60H15 #msc:60H05 #msc:60G51 #msc:60G20

paper · pdf

arxiv created 2026/08/06 · arxiv updated 2026/08/07

Abstract

Using the theory of stochastic integration in duals of nuclear spaces with respect to cylindrical martingale-valued measures, a vector-valued Itô formula is proved for generalized Itô processes defined with respect to these integrals. The abstract result is then applied to prove an Itô formula for Lévy-Itô processes defined with respect to Lévy processes taking values in the dual of a reflexive nuclear space.

Citations

• Itô's Formula for Itô processes defined with respect to a cylindrical-martingale valued measure
• Cylindrical Martingale-Valued Measures, Stochastic Integration and SPDEs
• Stochastic Integration and Stochastic PDEs Driven by Jumps on the Dual of a Nuclear Space
• Lévy Processes and Infinitely Divisible Measures in the Dual of a Nuclear Space
• Existence of Continuous and Càdlàg Versions for Cylindrical Processes in the Dual of a Nuclear Space
• An Itō formula in the space of tempered distributions
• Time Dependent Tempered Generalized Functions and Ito's Formula
• On the Itô-Wentzell formula for distribution-valued processes and related topics