Multi-layer perceptions can be dealt with pseudo-random numbers which are explained by beta minus expansivity and multiplicative linear congruent generators. The non-linear in data will require a hypothesis either of volatility feedback or leverage hypothesis when used for financial analysis. Volatility feedback essentially would mean the delta hedge is working and the market has a fine structure constant. The dimensions being added at edge we have embedding dimensions with n histories. As the investors attitude towards risk and expected returns are non-linear there is a distinction between non-linearity in mean and in variance as it is a multiple moment analysis.

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