Characterization of a wiener process taking values in a Hilbert space

This paper characterize wiener process by taking values in a Hilbert space. A standard wiener process is stochastic process {Wt }t≥0+ indesed by nonnegative real numbers t with the following properties: W0 = 0 With probability 1, the function t → Wt is continuous in t. The process {Wt }t≥0 has stationary, independent increments. The increments Wt+s- Ws has the NORMAL (0,t) distribution