While the signal field+ASE noise pass through a span of transmission fiber, a dispersion compensation grating and a fiber amplifier(with the generation of ASE noise), the nonlinear Fokker-Plank equations, describing the field’s probability transforms, are established and solved. Based on these statistical theories, the probability distributions of  the signal +ASE noise field through 50km NZDSF, a dispersion compensation grating and a fiber amplifier link, are obtained. The dispersion and nonlinear effects in transmission fiber induce frequency offsets in the probability distribution of field and they can not be dissipated by dispersion compensation. The generation of ASE noise in the amplifier will accelerate this frequency offset.