G{\^a}teaux type path-dependent PDEs and BSDEs with Gaussian forward processes
Probability
2019-08-01 v1
Abstract
We are interested in path-dependent semilinear PDEs, where the derivatives are of G{\^a}teaux 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.
Cite
@article{arxiv.1907.13366,
title = {G{\^a}teaux type path-dependent PDEs and BSDEs with Gaussian forward processes},
author = {Adrien Barrasso and Francesco Russo},
journal= {arXiv preprint arXiv:1907.13366},
year = {2019}
}