Large Deviation Principle for the Single Point Catalytic Super-Brownian Motion

#### K. Fleischmann, J. Xiong

2005, v.11, №3, 519-533

ABSTRACT

In the single point catalytic super-Brownian motion particles'' branch only if they meet the position of the single point catalyst. If the branching rate tends to zero, the model degenerates to the heat flow. We are concerned with large deviation probabilities related to this law of large numbers. To this aim the well-known explicit representation of the model by excursion densities is heavily used. The rate function is described by the Fenchel - Legendre transform of log-exponential moments described by a log-Laplace equation.

Keywords: point catalyst,superprocess,large deviations,exponentialmoments,singular catalytic medium,log-Laplace equation,representation by excursion densities