2019/06/22 by Grégoire Ferré, Gabriel Stoltz, Ferré, Grégoire +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Spectral Theory (math.SP) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.1906.09411
openalex publication_date 2019/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider large deviations of empirical measures of diffusion processes. In\na first part, we present conditions to obtain a large deviations principle\n(LDP) for a precise class of unbounded functions. This provides an analogue to\nthe standard Cram 'er condition in the context of diffusion processes, which\nturns out to be related to a spectral gap condition for a Witten-Schr "odinger\noperator. Secondly, we study more precisely the properties of the\nDonsker-Varadhan rate functional associated with the LDP. We revisit and\ngeneralize some standard duality results as well as a more original\ndecomposition of the rate functional with respect to the symmetric and\nantisymmetric parts of the dynamics. Finally, we apply our results to\noverdamped and underdamped Langevin dynamics, showing the applicability of our\nframework for degenerate diffusions in unbounded configuration spaces.\n