Fair enough. But the model that you have just programmed is _not_ the same as the math model that you posted from that blog. I must be confusing it with the Euler method, again.??

QuoteOriginally posted by: MattFQuoteOriginally posted by: StaleIntuitively: Looking at the filtration generated by this process, the information at time t does not contain any uncertainty if you use W_(t-1), so the state is perfectly well know. It should be W_t as you say Eduard.This comes from the defininition of the stochastic intergral, if you like to look it up Absolutely, and there's also a horrible confusion of whether t is a real-valued variable or indexing variable in the original formulation.'t' is just a variable from a continuous (or discrete) index set?So, W_t is just (sloppy) notation for N(0,1)?

it's very sloppy notation even though we know what it means:[$]S_t[$] means [$]S[$] at time [$]t[$], but [$]S_{t-1}[$] means [$]S[$] at time [$]t-\Delta t[$] not at time [$]t-1[$].

QuoteOriginally posted by: ppauperit's very sloppy notation even though we know what it means:[$]S_t[$] means [$]S[$] at time [$]t[$], but [$]S_{t-1}[$] means [$]S[$] at time [$]t-\Delta t[$] not at time [$]t-1[$].Indeed. So confusing and for no reason. Maybe SDE can learn from ODE/PDE notation?BTW I wonder who first concocted the idea of using S_t instead of the 99.99% more common S(t). I once attended a course by the late prof Neftci and when I saw W_t I thought it was dW/dt !!!The problem IMO is caused by blurring SDE in continuous time with its (FD) approximination at discrete time points. We really should not be having these discussions. Unambiguous notation // Rule: t is continuous time, t_n = n dt is a discrete time point, and S_n ~ S(t_n). And using S for both cases is scary. Better X(t) for the SDE and Y_n for its approximation."Young man, in mathematics you don't understand things. You just get used to them. " John von Neumann.

Another doubt(?) W_(t-1) 't' has units in time '1' is dimensionlessIs t -1 allowed?