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 defin...

A Hilbert-valued stochastic integration is defined for an integrator that is a cylindrical fractional Brownian motion in a Hilbert space. Since the integrator is not a semimartingale for the fractional Brownian motions considered, a different definition of integration is required. Both deterministic and stochastic operator-valued integrands are used. The approach to integration has an analogue ...

In this paper, we introduce the idea of stochastic integrals with respect to an increasing process in the G-framework and extend G-Itô’s formula. Moreover, we study the solvability of the scalar valued stochastic differential equations driven by G-Brownian motion with reflecting boundary conditions (RGSDEs).