Spin torque in the framework of random magnetization dynamics driven by a jump-noise process

It is demonstrated that the Slonczewski spin-torque term can be naturally derived from the equation for magnetization dynamics driven by a jump-noise process. The central point of the derivation is the modification of transition probability rate of the jump-noise process caused by spin-polarized current injection. This modification results in two distinct terms in the expected value of the jump-noise process: the traditional one corresponding to the Landau-Lifshitz damping and another one representing the Slonczewski spin-torque term.