Abstract
Counterexamples in the theory of stochastic maximal regularity.
We show that a bounded H00 calculus is not enough to ensure stochastic maximal regularity for the generator A of an analytic semigroup on a UMD space with type 2.
The problem even occurs for spaces X such as L_2(L_r) or L_2 + L_r for r>2 and A the Laplace operator L_p(R,X).
These are joint results with E. Lorist, J van Neerven and M. Veraar from Delft University of Technology.