2 citations · 5 across the 8 of their papers we have counts for
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Numerical computation of probabilities for nonlinear SDEs in high dimension using Kolmogorov equation
Franco Flandoli, Dejun Luo, Cristiano Ricci
Stochastic Differential Equations (SDEs) in high dimension, having the structure of finite dimensional approximation of Stochastic Partial Differential Equations (SPDEs), are consi…
Epidemic Models as Scaling Limits of Individual Dynamics
Franco Flandoli, Francesco Grotto, Andrea Papini +1
Infection spread among individuals is modelled with a continuous time Markov chain, in which subject interactions depend on their distance in space. The well known SIR model and no…
A mean-field approach to self-interacting network, convergence and regularity
Rémi Catellier, Yves D'Angelo, Cristiano Ricci
The propagation of chaos property for a system of interacting particles, describing the spatial evolution of a network of interacting filaments is studied. The creation of a networ…
On the relation between the Girsanov transform and the Kolmogorov equations for SPDEs
Franco Flandoli, Dejun Luo, Cristiano Ricci
The Girsanov transform and Kolmogorov equations are two useful methods for studying SPDEs. It is shown that, under suitable conditions, the series expansion obtained from the Girsa…
On the Macroscopic limit of Brownian Particles with local interaction
Franco Flandoli, Marta Leocata, Cristiano Ricci
An interacting particle system made of diffusion processes with local interaction is considered and the macroscopic limit to a nonlinear PDE is investigated. Few rigorous results e…
A numerical approach to Kolmogorov equation in high dimension based on Gaussian analysis
Franco Flandoli, Dejun Luo, Cristiano Ricci
For Kolmogorov equations associated to finite dimensional stochastic differential equations (SDEs) in high dimension, a numerical method alternative to Monte Carlo simulations is p…
The Navier-Stokes-Vlasov-Fokker-Planck system as a scaling limit of particles in a fluid
Franco Flandoli, Marta Leocata, Cristiano Ricci
Convergence of a system of particles, interacting with a fluid, to Navier-Stokes-Vlasov-Fokker-Planck system is studied. The interaction between particles and fluid is described by…
The Vlasov-Navier-Stokes equations as a mean field limit
Franco Flandoli, Marta Leocata, Cristiano Ricci
Convergence of particle systems to the Vlasov-Navier-Stokes equations is a difficult topic with only fragmentary results. Under a suitable modification of the classical Stokes drag…