Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations

2014/11/28 by Andrea Cosso, Cristina Di Girolami, Cosso, Andrea +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1411.8000

openalex publication_date 2014/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper reminds the basic ideas of stochastic calculus via regularizations in Banach spaces and its applications to the study of strict solutions of Kolmogorov path dependent equations associated with "windows" of diffusion processes. One makes the link between the Banach space approach and the so called functional stochastic calculus. When no strict solutions are available one describes the notion of strong-viscosity solution which alternative (in infinite dimension) to the classical notion of viscosity solution.

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