14 citations · 24 across the 8 of their papers we have counts for
8 papers
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…
Approximation of non-linear SPDEs with additive noise via weighted interacting particles systems: the stochastic McKean-Vlasov equation
Letizia Angeli, Dan Crisan, Martin Kolodziejczyk +1
This paper is devoted to the problem of approximating non-linear Stochastic Partial Differential Equations (SPDEs) via interacting particle systems. In particular, we consider the…
Stochastic Calculus in Infinite Dimensions and SPDEs
Daniel Goodair
These notes rigorously construct the stochastic integral of a Hilbert Space valued process driven by a Cylindrical Brownian Motion. We expand upon this stochastic calculus to prese…
Uniform in time estimates for the weak error of the Euler method for SDEs and a Pathwise Approach to Derivative Estimates for Diffusion Semigroups
D. Crisan, P. Dobson, M. Ottobre
We present a criterion for uniform in time convergence of the weak error of the Euler scheme for Stochastic Differential equations (SDEs). The criterion requires i) exponential dec…
Long-time behaviour of degenerate diffusions: UFG-type SDEs and time-inhomogeneous hypoelliptic processes
T. Cass, D. Crisan, P. Dobson +1
We study the long time behaviour of a large class of diffusion processes on , generated by second order differential operators of (possibly) degenerate type. The operators tha…
Pointwise Gradient Bounds for Degenerate Semigroups (of UFG type)
Dan Crisan, Michela Ottobre
In this paper we consider diffusion semigroups generated by second order differential operators of degenerate type. The operators that we consider do not, in general, satisfy the H…