4 papers
Functional integration by parts formulae for stochastic Volterra processes
Alexandre Pannier
We investigate integration by parts (IBP) formulae for stochastic Volterra equations and we establish the smoothing effect of the expectation. Due to the inherent path-dependent dy…
A path-dependent PDE solver based on signature kernels
Alexandre Pannier, Cristopher Salvi
We develop a kernel-based solver for path-dependent PDEs (PPDEs) along with a convergence theory. Our numerical scheme leverages signature kernels, a recently introduced class of k…
Kolmogorov equations for stochastic Volterra processes with singular kernels
Ioannis Gasteratos, Alexandre Pannier
We associate backward and forward Kolmogorov equations to a class of fully nonlinear Stochastic Volterra Equations (SVEs) with convolution kernels that are singular at the orig…
A BDG inequality for stochastic Volterra integrals
Alexandre Pannier
We establish Burkholder-Davis-Gundy-type inequalities for stochastic Volterra integrals with a completely monotone convolution kernel, which may exhibit singular behaviour at the o…