Large deviations for invariant measures of stochastic reaction–diffusion systems with multiplicative noise and non-Lipschitz reaction term

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Existence and Uniqueness of Invariant Measures for Stochastic Reaction–Diffusion Equations in Unbounded Domains (2014, unknown): “, in the works of Da Prato and Zabczyk [11,12] or Cerrai [6]) cannot be formally applied in the particular setting due to the specific choice of the operator, the weight and the boundary conditions.”
Global solutions to stochastic reaction–diffusion equations with super-linear drift and multiplicative noise (2019, background): “Several papers in the literature discuss stochastic PDEs with locally Lipschitz coefficients that have polynomial growth and/or satisfy certain monotonicity conditions (see [4, 11, 18, 21, 22], for instance).”
A Khasminskii type averaging principle for stochastic reaction–diffusion equations (2008, methodology): “…proved that an averaging principle is satisfied by using a completely different approach based on Kolmogorov equations and martingale solutions of stochastic equations, which is more in the spirit of the general method introduced by Papanicolaou, Strook and Varadhan in their paper [24] of 1977.”
Stochastic Reaction-diffusion Equations Driven by Jump Processes (2010, unknown): “19) was studied by Cerrai in [20] when each L is a Wiener process.”