Linear transformations of Wiener process that born Wiener process, Brownian bridge or Ornstein-Uhlenbeck process

summary:The paper presents a discussion on linear transformations of a Wiener process. The considered processes are collections of stochastic integrals of non-random functions w.r.t. Wiener process. We are interested in conditions under which the transformed process is a Wiener process, a Brownian bridge or an Ornstein –Uhlenbeck process.