4 papers
Structured Neural SDEs for Functional Calibration
Francesco Piatti, Andrea Iannucci, Thomas Cass
Neural Stochastic Differential Equations (Neural SDEs) provide flexible continuous-time generative models, but generic neural drift and diffusion networks are costly to simulate on…
Signature Kernel and Schwinger-Dyson Kernel Equations as Two-Parameter Rough Differential Equations
Thomas Cass, Dan Crisan, Andrea Iannucci +1
We develop a rough-path framework for two-parameter rough differential equations on rectangular and simplicial domains, motivated by the signature kernel and Schwinger--Dyson kerne…
Nonlinear Stochastic Filtering with Volterra Gaussian noises
Thomas Cass, Dan Crisan, Andrea Iannucci
We develop a nonlinear filtering theory for signal-observation systems driven by Volterra Gaussian processes, covering both the Young and genuinely rough regimes. The dynamics are…
Pathwise Optimal Control and Rough Fractional Hamilton-Jacobi-Bellman Equations for Rough-Fractional Dynamics
Andrea Iannucci, Dan Crisan, Thomas Cass
In this work, we investigate the degeneracy problem in pathwise control, extending the framework developed in \cite{allan2020pathwise} to a more general class of driving signals an…