Verification theorem related to a zero sum stochastic differential game via Fukushima-Dirichlet decomposition. Verification theorem

Carlo Ciccarella and Francesco Russo
soumis
Type de publication :
Article (revues avec comité de lecture)
HAL :
hal-04637897
arXiv :
assets/images/icons/icon_arxiv.png 2407.06243
Mots clés :
Stochastic differential games; Stochastic control; Verification theorem; Weak Dirichlet processes
Résumé :
We establish a verification theorem, inspired by those existing in stochastic control, to demonstrate how a pair of progressively measurable controls can form a Nash equilibrium in a stochastic zero-sum differential game. Specifically, we suppose that a pathwise-type Isaacs condition is satisfied together with the existence of what is termed a quasi-strong solution to the Bellman-Isaacs (BI) equations. In that case we are able to show that the value of the game is achieved and corresponds exactly to the unique solution of the BI equations. Those have also been applied for improving a well-known verification theorem in stochastic control theory. In so doing, we have implemented new techniques of stochastic calculus via regularizations, developing specific chain rules.
BibTeX :
@article{Cic-Rus-2200,
    author={Carlo Ciccarella and Francesco Russo },
    title={Verification theorem related to a zero sum stochastic 
           differential game via Fukushima-Dirichlet decomposition. 
           Verification theorem },
    year={soumis },
    month={7},
}