We consider a standard Brownian motion W ¯ ¯ t n (a.k.a. Wiener Process) evaluated on a time mesh sequence t 0 = 0 < t 1 < ⋯ ⋯ < t n < ⋯ ⋯ with a given time step t n − − t n − − 1 = h . We choose c ( x ) = x in equation (1), we replace b ( x ) and σ by b ( x ) × × h and σ σ × × h , and we write X ¯ ¯ t n instead of X ¯ ¯ n the values of the random states evaluated at the time step t n . Recalling that ( W ¯ ¯ t n + 1 − − W ¯ ¯ t n ) are independent centered Gaussian random variables with variance t n − − t n − − 1 = h , the resulting equation can be rewritten in the following form