I don't post a ton, but I believe this is a waste of most of these guys' time. You require too much prerequisite information. This should really be moved to the 'Student Forum' where it will be appropriately ignored as it has been covered by many texts already. For stock options, start with a Bachelier (normal) model, do simple price diffs, and then find out why you don't want that. Then move to logReturns where when you take the log(Px) then the diffs are actually log returns with some nice features dLogPx = (log(Px_1) - log(Px_0)) = log(Px_1/Px_0) . Doing this stuff over time, etc.... As was said earlier. Kindergarten stuff. Maybe I'd give it 8th grade, but I'm American. So everywhere else it may be like 4th grade
But this was not the question raised by my OP, which was about the semantics of sigma root t, i.e. its meaning. The fact my question has so consistently been misunderstood kind of answers my question.
If you look at the actual application of the heat equation, i.e. where there are terms referring to heat flux (flow) and so on, tells you that there are entirely different ways of *interpreting* the terms.