Systems confined by pusher multiplicative noises

We frequently employ the intuitive concept that a multiplicative noise can expel a system towards the field values for which intensity is negligible. This process applies even when such noise effects are opposed to the deterministic forces. In addition, it has been stated that a system may be confined by such noise within a field values region, distant from the stationary homogeneous solutions. In order to promote or explain noise-induced ordering phase transitions, the gradient of the multiplicative factor of noise is employed as if it were a force. However, there has not been a thorough study of this concept in the literature to date. In this paper, we conduct such a study.