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

2016
Publication type:
Paper in peer-reviewed journals
Workshop:
Probability on Algebraic and Geometric Structures, June 5-7 2014
Publisher:
Contemporary Mathematics 668
arXiv:
images/icons/icon_arxiv.png 1411.8000
Keywords :
Stochastic calculus via regularization in Banach spaces; path dependent Komogorov equation; functional Itô calculus.
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.
BibTeX:
@article{Cos-DiG-Rus-2016,
    author={Andrea Cosso and Cristina Di Girolami and Francesco Russo },
    title={Calculus via regularizations in Banach spaces and 
           Kolmogorov-type path-dependent equations },
    year={2016 },
    volume={668 },
    pages={43--65},
}