Gâteaux type path-dependent PDEs and BSDEs with Gaussian forward processes

Adrien Barrasso and Francesco Russo

january, 2022

Publication type:

Paper in peer-reviewed journals

Journal:

Stochastics and Dynamics, vol. 22, pp. 2250007

DOI:

10.1142/S0219493722500071

HAL:

hal-02197479

arXiv:

1907.13366

Keywords :

Gaussian processes; Volterra processes; path-dependent PDEs; decoupled mild solutions; BSDEs.

Abstract:

We are interested in path-dependent semilinear PDEs, where the derivatives are of Gâteaux type in specific directions k and b, being the kernel functions of a Volterra Gaussian process X. Under some conditions on k, b and the coefficients of the PDE, we prove existence and uniqueness of a decoupled mild solution, a notion introduced in a previous paper by the authors. We also show that the solution of the PDE can be represented through BSDEs where the forward (underlying) process is X.

BibTeX:

@article{Bar-Rus-2022,
    author={Adrien Barrasso and Francesco Russo },
    title={Gâteaux type path-dependent PDEs and BSDEs with Gaussian 
           forward processes },
    doi={10.1142/S0219493722500071 },
    journal={Stochastics and Dynamics },
    year={2022 },
    month={1},
    volume={22 },
    pages={2250007},
}