Large deviation principle for the single point catalytic super-Brownian motion
- Fleischmann, Klaus
- Xiong, Jie
2010 Mathematics Subject Classification
- 60K35 60J80
- Point catalyst, superprocess, large deviations, exponential moments, singular catalytic medium, log-Laplace equation, representation by excursion densities
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.
- Markov Process. Related Fields, 11 (2005), pp. 519-533.