Technical Forum • Re: Breakthrough in the theory of stochastic differential equations and their simulation

Let us solve a toy problem with four correlation parameters that are initially chosen in a way that their sum squared is already one i.e. \[\,{\rho_1}^2\,+\,{\rho_2}^2\,+\,{\rho_3}^2\,+\,{\rho_4}^2\,=\,1\,\] obviously so that squared sum remains unity, any changes would have to be made in a way that \[\,\Delta{\rho_1}^2\,+\,\Delta{\rho_2}^2\,+\,\Delta{\rho_3}^2\,+\,\Delta{\rho_4}^2\,=\,0\,\] For this to hold, the increase in sum squared over increasing parameters has to be equal to decrease in s