Markov Chain Approximation of Sticky Diffusions and Hamilton-Jacobi-Bellman Equations on Networks

Alessio Basti; Jules Berry; Fabio Camilli

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arXiv · 2607.26709

Markov Chain Approximation of Sticky Diffusions and Hamilton-Jacobi-Bellman Equations on Networks

Alessio Basti·Jules Berry·Fabio Camilli

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Abstract

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 residence mechanism at the vertex, while the motion along the edges follows an Euler-Maruyama-type update at the diffusive scale. We prove that the associated time-interpolated chain converges in distribution to the limiting diffusion in the Skorokhod space using the Ethier-Kurtz framework. Based on this construction, we derive a fully discrete semi-Lagrangian scheme for Hamilton-Jacobi-Bellman equations on networks and establish its convergence using viscosity solution techniques.

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Alessio Basti, Jules Berry, Fabio Camilli. 2026-07-29. Markov Chain Approximation of Sticky Diffusions and Hamilton-Jacobi-Bellman Equations on Networks. https://arxiv.org/abs/2607.26709

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