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arXiv · 2610.39903

Interacting particles in random irregular media

Luca Bondi·Elena Issoglio·Francesco Russo
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Abstract

In this paper, we first develop novel tools of independent interest in the field of stochastic calculus related to SDEs with distributional drift, namely the formulation of a quasi-Stroock-Varadhan martingale problem in the sense that the test functions are of class $C^{1,2}$ instead of solutions of Kolmogorov type PDE. This has several applications, among which, the time restriction and the notion of conditional rough martingale problem and related solution.

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Luca Bondi, Elena Issoglio, Francesco Russo. 2026-10-29. Interacting particles in random irregular media. https://arxiv.org/abs/2610.39903

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