Historical share's behavior accounting

The models where stock is a lognormal distributed random process are the routine ones. But these models ignore a possible sensitivities of a share's price to the last quotations. In present paper a mathematical model of such kind “memory” accounting is proposed. The model is in concordance with basis postulates of financial mathematics. A contribution of historical stock's behavior is taking into account as additive component in stochastic differential. The effect of the “memory” presence is characterized by time interval $\tau$ that defines the size of the “memory” in the past. A size of the contribution from moment passed is described by weight function.