PR ] 3 1 Ju l 2 01 9 Gâteaux type path-dependent PDEs and BSDEs with Gaussian forward processes

@inproceedings{Barrasso2019PR3,
  title={PR ] 3 1 Ju l 2 01 9 G{\^a}teaux type path-dependent PDEs and BSDEs with Gaussian forward processes},
  author={Adrien Barrasso and Francesco Russo},
  year={2019}
}
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 . MSC… CONTINUE READING