Space-time regularity of catalytic super-Brownian motion
- Zähle, Henryk
2010 Mathematics Subject Classification
- 60H15 60K35 60G57 60J80
- catalytic super-Brownian motion, cumulant equation, martingale problem, collision local time, stochastic partial differential equation
We focus on the question, for which catalysts does the catalytic super-Brownian motion in $real^1$ have a jointly continuous space-time Lebesgue density? As it turns out, nearly all non-atomic catalysts provide such a regular density which can be characterized as the unique solution to a stochastic partial differential equation driven by a degenerated space-time white noise.