  It seems that a stochastic system must be a nonlinear one to observe the
phenomenon, noise induced transition. But in the present paper, we have
demonstrated that the phenomenon may be observed even in a linear stochastic
process where both deterministic and stochastic parts are linear functions of
the relevant phase space variables. The shape of the stationary distribution of
particles (which are confined in a harmonic potential) may change on increasing
the strength of the applied fluctuating magnetic field. The probability density
may vary non monotonically with an increase in the coordinate of a Brownian
particle. Thus the distribution of particles may deviate strongly from the
Boltzmann one and it is a unique signature of the fluctuating magnetic field.
Then we are motivated strongly to study the distribution of particles in a
nonlinear stochastic system where the Brownian particles are confined in a
bi-stable potential energy field in the presence of the fluctuating magnetic
field. With a relatively large strength of the fluctuating field, the
distribution of particles may be a strange one where many islands may appear
which are not expected from the given potential energy field. It may offer an
explanation to describe the phenomenon, the reduction of the current in a
semiconductor in the presence of a time dependent magnetic field.
