Brownian Motion, 2nd Edition

4 The canonical model

Often we encounter the statement ‘Let X be a random variable with law μ’ where μ is an a priori given probability distribution. There is no reference to the underlying probability space ( ), and actually the nature of this space is not important: While X is defined by the probability distribution, there is considerable freedom in the choice of our model (). The same situation is true for stochastic processes: Brownian motion ...