Abstract
Local large deviation principles are established in dimensions d≥3 for the super Brownian motion with random immigration X ϱ t , where the immigration rate is governed by the trajectory of another super-Brownian motion ϱ. The speed function is t for d≥4 and t1/2 for d=3, compared with the existing results, the interesting phenomenon happened in d=4 with speed t (although only the upper large deviation bound is derived here) is just because the structure of this new model: the random immigration “smooth” the critical dimension in some sense. The rate function are characterized by an evolution equation.
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