Stochastic propagation of fluxons on Josephson lines

In this paper, the fluxons propagation on Josephson junction is modeled by the nonlinear Sine-Gordon equation which has received much attention in recent years. The stochastic surface current is studied under the effect of stochastic propagation velocity. The probability density function of the surface current is derived using successive random process transformation. Furthermore, the stochastic moments of the surface current are computed for some case studies.