Particle Filters for Multiscale Diffusions

We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the optimal filter.

💡 Research Summary

The paper addresses the problem of filtering partially observed multiscale stochastic diffusion processes, where observations are available only at discrete times on the slow time scale. Classical sequential Monte‑Carlo (SMC) or particle‑filter methods would require simulating both the slow variables and the fast variables with a very small time step, leading to prohibitive computational cost and severe particle degeneracy. To overcome these difficulties, the authors propose a novel particle‑filter algorithm that explicitly exploits the scale separation.

The model under consideration is of the form

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