Ну, во-первых, если ценовое распределение не подчиняется нормальному закону, из этого вовсе не следует, что оно неслучайно.
Yes, exactly. I mentioned the Gaussian distribution because it is the most popular, considering the scale-invariant random distributions. In practice one should care about the scale properties of the cumulants of distribution and formulate the strategy in a way that trades towards the IID (Independent Identically Distributed functions of price increments). I can do this precisely only in formula language.
то
произойдет, если арбитраж начнет разъезжаться и распределение начнет приобретать все менее и менее гауссову форму?
I do not expect anything of this kind on the average.
время полета из NYC в Chicago 3 ч. 40 мин. Каково матожидание времени, которое мы проведем в таком полете?
If there exists a small probability that a plane crashes, then the expectation value of your time flight is equal to infinity (sometimes I think that the expectation time of waiting for a bus in Russia is also equal to infinity, but that is out of topic). It is good that you mentioned that point. The trading strategy should be based on a statistics which is RARE but not UNIQUE. That is why one always should throw away from time series the extreme events, crises, panics, plane crashes, etc.
Sometimes one can use the extreme events as well for making money (e.g. predicting the crises by using some model assumtions), but this is another story and another strategy.
