Gâteaux type path-dependent PDEs and BSDEs with Gaussian forward processes
january, 2022
Publication type:
Paper in peer-reviewed journals
Journal:
Stochastics and Dynamics, vol. 22, pp. 2250007
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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}, }