N,Although your quotes:QuoteOriginally posted by: NNo, the process is continuous. The particular solution to the heat equation is e^-at. Adding boundary conditions, we get the expected Gaussian temperature/time curve. [The equivalent circuit is a network of resistors with capacitors at each node, in case you're an EE] Notice that this particular solution also applies to compound interest. In one case the 'rate' is heat conduction and with the other it's the compound interest rate. All Lie groups have a 'rate' (or infinitesimal automorphism ) including this most simple example. Please note that not only are these processes continous, but there is no noise (BM). Aslo note that only rational numbers are needed for the math.And:Look, the manifold I just described is clearly continuous, has a rational number domain, is deterministic, is fully integrable and has single discrete state (the "rate"). Since probability cannot be complex, this smooth manifold is the only manifold where probability can be defined.Fermion, it may not be obvious, but if probability is a rational number then probability *is* frequency counting, right? Black-Scholes is defined on this manifold. (although the model itself may not be robust enough).So far, there's no Brownian motion.are a bit more elaborated than your previous quotes, I'd still like you to give me some reference that takes a book like, let's say, Avellaneda's "Quantitative Modeling of Derivative Securities" ,and shows where things are wrong, and, most importantly, what would be the correct way of price derivatives instead.My EE course is 15 years behind me and I've almost succeeded in forgetting everything but the software part, so mentioning resistors triggers bad memory circuits for me.