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New averaging principle for fast-slow SDEs with degenerate noise

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A new research paper introduces a strong averaging principle for fast-slow stochastic differential equations (SDEs). This principle applies to systems where the time-scale separation increases over time, and the noise can be degenerate. The approach relies on the dissipativity of the frozen fast dynamics, allowing for degenerate diffusion coefficients. The paper establishes a maximal L^p-estimate between the slow variable and the averaged ordinary differential equation (ODE) at late times, demonstrating a classical strong convergence rate of 1/2. This work provides criteria for identifying potential limit points and for convergence towards asymptotically stable equilibria of the slow variable by analyzing the averaged equation's dynamics. AI

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New averaging principle for fast-slow SDEs with degenerate noise

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COVERAGE [1]

  1. arXiv stat.ML TIER_1 English(EN) · Sebastian Kassing, Asuto Miwa ·

    Strong Averaging Principle and Long-Time Dynamics for Fast-Slow SDEs with Increasing Time-Scale Separation and Degenerate Noise

    arXiv:2608.23462v1 Announce Type: cross Abstract: We establish a strong averaging principle for fast-slow stochastic differential equations with a time-dependent scale-separation parameter $(\varepsilon_t)_{t \geq 0}$ satisfying $\varepsilon_t \to 0$ as $t \to \infty$. In contras…

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