Effect of Noise on Gradient Systems

Abstract :-
In this paper, we generalize our work to perturbed gradient systems (PGS). For original gradient systems (GS), the change of a vector x(t) at time t is defined as the gradient vector of a function F(x) times a small negative constant. For PGS, it is assumed that the vector x(t) is perturbed by mean zero Gaussian noise. The noise can either be multiplicative or additive. In this paper, the corresponding energy functions for both cases are derived. It is found that their energy functions are very difference from F(x). Continue reading Effect of Noise on Gradient Systems