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math.NA2026
Markov Chain Approximation of Sticky Diffusions and Hamilton-Jacobi-Bellman Equations on Networks
Alessio Basti, Jules Berry, Fabio Camilli
We propose a discrete Markov-chain approximation of diffusion processes on networks with both Kirchhoff and sticky vertex conditions. Stickiness is modeled by a probabilistic resid…
math.NA2026
Kolmogorov -entropy of numerical solutions for scalar conservation laws with convex flux
Fabio Ancona, Alessio Basti, Fabio Camilli
Building on the information-theoretic perspective of P.~D.~Lax [\textit{Proc.\ Sympos., Math.\ Res.\ Center, Univ.\ Wisconsin}, 1978], we establish a two-sided quantitative compact…
math.NA2026
A Mean Field Games Perspective on Evolutionary Clustering
Alessio Basti, Fabio Camilli, Adriano Festa
We propose a control-theoretic framework for evolutionary clustering based on quasi-stationary Mean Field Games. Each cluster is represented by a probability density whose evolutio…