Singular Stochastic Differential Equations for Time Evolution of Stocks Within Non-white Noise Approach

The influence of non-linear terms and non-white noise terms on stochastic differential equation model for time evolution of prices of the market is investigated with aim to analyse the effect generated on exponent of the long-tail distribution of the probability density of the returns and Hurst index. In particular, whether the model proposed is adequate as a possible mathematical model for description of the market either if it satisfies to the stylized facts obeyed by the financial markets as the long-tail distribution of the returns, which must obey to the inverse cubic law observed.