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math.PR2026
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…
math.PR2025
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…
math.PR2025
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…