  In this work cylindrical Wiener processes on Banach spaces are defined by
means of cylindrical stochastic processes, which are a well considered
mathematical object. This approach allows a definition which is a simple
straightforward extension of the real-valued situation. We apply this
definition to introduce a stochastic integral with respect to cylindrical
Wiener processes. Again, this definition is a straightforward extension of the
real-valued situation which results now in simple conditions on the integrand.
In particular, we do not have to put any geometric constraints on the Banach
space under consideration. Finally, we relate this integral to well-known
stochastic integrals in literature.
