发表机构
CY Cergy Paris Université（塞吉-巴黎大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究圆上一维扩散过程Donsker-Varadhan速率函数在噪声消失时的渐近行为，发现两种表示极限不总一致，导致无穷维空间中的连续与不连续现象，并利用Γ-收敛在大偏差原理中取极限。
AI 中文摘要
我们研究了圆上一维扩散过程Donsker-Varadhan大偏差原理中速率函数的消失噪声极限。众所周知，速率函数既可以表示为扰动无穷小生成元主特征值的Legendre变换，也可以通过变分公式表示。我们分析了当噪声前的参数趋于零时主特征值的渐近行为，并将该极限的Legendre变换与变分表示取极限所得的表达式进行比较。我们特别证明了所得表达式并不总是重合，从而在无穷维函数空间中导致连续性和不连续性现象。此外，我们利用上述分析，借助Γ-收敛的概念，在大偏差原理中取极限。
英文摘要
We study the vanishing-noise limit of the rate function for the Donsker-Varadhan large deviation principle for one-dimensional diffusion processes on a circle. As is well known, the rate function can be represented either as the Legendre transform of the principal eigenvalue of the perturbed infinitesimal generator or by a variational formula. We analyze the asymptotic behavior of the principal eigenvalue as the parameter in front of the noise goes to zero and compare the Legendre transform of the limit with the expression obtained as the limit of the variational representation. We prove, in particular, that the resulting expressions do not always coincide, leading to continuity and discontinuity phenomena in infinite-dimensional functional spaces. Moreover, we use the previous analysis to pass to the limit in the LDP, using the notion of Γ-convergence.
Journal refElectronic Journal of Differential Equations, Vol. 2026 (2026), No. 71, pp. 1-33
