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- W4295698811 abstract "In this paper, we study the Onsager-Machlup function and its relationship to the Freidlin-Wentzell function for measures equivalent to arbitrary infinite dimensional Gaussian measures. The Onsager-Machlup function can serve as a density on infinite dimensional spaces, where a uniform measure does not exist, and has been seen as the Lagrangian for the ``most likely element. The Freidlin-Wentzell rate function is the large deviations rate function for small-noise limits and has also been identified as a Lagrangian for the ``most likely element. This leads to a conundrum - what is the relationship between these two functions? We show both pointwise and $Gamma$-convergence (which is essentially the convergence of minimizers) of the Onsager-Machlup function under the small-noise limit to the Freidlin-Wentzell function - and give an expression for both. That is, we show that the small-noise limit of the most likely element is the most likely element in the small noise limit for infinite dimensional measures that are equivalent to a Gaussian. Examples of measures include the law of solutions to path-dependent stochastic differential equations and the law of an infinite system of random algebraic equations." @default.
- W4295698811 created "2022-09-14" @default.
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- W4295698811 date "2022-09-09" @default.
- W4295698811 modified "2023-09-25" @default.
- W4295698811 title "The Small-Noise Limit of the Most Likely Element is the Most Likely Element in the Small-Noise Limit" @default.
- W4295698811 doi "https://doi.org/10.48550/arxiv.2209.04523" @default.
- W4295698811 hasPublicationYear "2022" @default.
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