On stochastic convolution in banach spaces and applications

Stochastic evolution equations are studied in M-type 2 Banach spaces framework. Using factorization method and Burkholder inequality we prove regularity properties of stochastic convolution processes. We prove also existence of local and global solutions with close to optimal regularity. We show that solution with cylindrical Wiener process can be approximated by solutions with finite dimensional Wiener processes. Application to reaction diffusion equations are presented