Functional It =o calculus in Hilbert spaces and application to\n path-dependent Kolmogorov equations

2016/06/20 by Mauro Rosestolato, Rosestolato, Mauro
Computer Science · Economics, Econometrics and Finance · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1606.06326

openalex publication_date 2016/06/20 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

Recently, functional It =o calculus has been introduced and developed in\nfinite dimension for functionals of continuous semimartingales. With different\ntechniques, we develop a functional It =o calculus for functionals of Hilbert\nspacevalued diffusions. In this context, we first prove a path-dependent\nIt =o's formula, then we show applications to classical solutions of\npath-dependent Kolmogorov equations in Hilbert spaces and derive a Clark-Ocone\ntype formula. Finally, we explicitly verify that all the theory developed can\nbe applied to a class of diffusions driven by SDEs with a path-dependent drift\n(suitably regular) and constant diffusion coefficient.\n

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