Linear Langevin equation with time-dependent drift and multiplicatie noise term: exact study

摘要

We investigate a linear Langevin equation with multiplicative noise term and time-dependent drift. This system extends the system analyzed by Lillo and Mantegna [Phys. Rev. E 61 (2000) R467]. We calculate the average of every moments and the variance of the system. We show that the system, with a particular choice of γ(t), can describe different processes like diffusive, subdiffusive and superdiffusive. Other kinds of processes can also been obtained. We also show that the multiplicative noise term has the effect of splitting the peak of transition probability P(x,t|x',t'), at a fixed time, into two peaks in coordinate.