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arXiv · 1907.13366

G{â}teaux type path-dependent PDEs and BSDEs with Gaussian forward processes

Adrien Barrasso·Francesco Russo
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Abstract

We are interested in path-dependent semilinear PDEs, where the derivatives are of G{â}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.

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Adrien Barrasso, Francesco Russo. 2019-07-31. G{â}teaux type path-dependent PDEs and BSDEs with Gaussian forward processes. https://arxiv.org/abs/1907.13366

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