2016/06/13 by Giorgio Fabbri, Fabbri, Giorgio, Francesco Russo +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.1606.03828
openalex publication_date 2016/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking values in a Banach space H, is the sum of a local martingale and a suitable orthogonal process. The concept of weak Dirichlet process fits the notion of convolution type processes, a class including mild solutions for stochastic evolution equations on infinite dimensional Hilbert spaces and in particular of several classes of stochastic partial differential equations (SPDEs). In particular the mentioned decomposition appears to be a substitute of an Itô's type formula applied to f (t, X(t)) where f : [0, T ] × H → R is a C 0,1 function and X a convolution type processes.