Infinite dimensional weak Dirichlet processes, stochastic PDEs and optimal control - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2014

Infinite dimensional weak Dirichlet processes, stochastic PDEs and optimal control

Abstract

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 Hilbert space $H$, is the sum of a local martingale and a suitable "orthogonal" process. The new concept is shown to be useful in several contexts and directions. On one side, the mentioned decomposition appears to be a substitute of an Itô type formula applied to $f(t, \X(t))$ where $f:[0,T] \times H \rightarrow \R$ is a $C^{0,1}$ function and, on the other side, the idea of weak Dirichlet process fits the widely used notion of "mild solution" for stochastic PDE. As a specific application, we provide a verification theorem for stochastic optimal control problems whose state equation is an infinite dimensional stochastic evolution equation.
Fichier principal
Vignette du fichier
Stoch-Verif27fev2014FR.pdf (508.99 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00720490 , version 1 (24-07-2012)
hal-00720490 , version 2 (12-06-2016)

Identifiers

Cite

Giorgio Fabbri, Francesco Russo. Infinite dimensional weak Dirichlet processes, stochastic PDEs and optimal control. 2014. ⟨hal-00720490v2⟩
281 View
379 Download

Altmetric

Share

Gmail Facebook X LinkedIn More