Heat equation with strongly inhomogeneous noise
- Zähle, Henryk
2010 Mathematics Subject Classification
- 60H15 35R60 60H20 60J80
- stochastic partial differential equation, martingale problem, singularmeasure, catalytic super-Brownian motion
We consider the stochastic heat equation in dimension one with singular drift and driven by an inhomogeneous space-time white noise whose quadratic variation measure is not absolutely continuous w.r.t. Lebesgue measure, neither in space nor in time. Under various assumptions we give statements on strong and weak existence as well as strong and weak uniqueness of continuous solutions.