Systems of small-noise stochastic reaction-diffusion equations satisfy a large deviations principle that is uniform over all initial data
Salins, Michael
This paper proves three uniform large deviations results for a system of stochastic reaction--diffusion equations exposed to small multiplicative noise. If the reaction term can be written as the sum of a decreasing function and a Lipschitz continuous function and the multiplicative noise term is Lipschitz continuous, then the system satisfies a large deviations principle that is uniform over bounded subsets of initial data. Under the stronger assumption that the multiplicative noise term is uniformly bounded, the large deviations principle is uniform over all initial data, not just bounded sets. Alternatively, if the reaction term features super-linear dissipativity, like odd-degree polynomials with negative leading terms do, and the multiplicative noise term is unbounded, but does not grow too quickly, then the large deviations principle is uniform over all initial data.
↧