Large Deviation Principle for Some Measure-Valued Processes

Moderate deviation principle for a class of stochastic partial differential equations

“…Analogous to Lemma 6 of [7] we have that for the set of functions with finite variations, A, the map ξ :…”

“…This rate of convergence is best given by the large deviation principle (LDP). In [7], we achieved the LDP for SBM and FVP as the above mentioned rates go to zero and obtained an explicit form of the rate of convergence for each model. However, the topology introduced there is not the natural one.…”

Super-Brownian motion as the unique strong solution to an SPDE

“…As is well known, LDP for general FV process is a long standing open problem (some partial results were obtained by Dawson and Feng [4,5], and Feng and Xiong [8] for neutral FV processes, and Xiang and Zhang [27] for the case when the mutation operator tends to 0). This application will be presented in a joint work of Fatheddin and Xiong [7].…”