4 The canonical model

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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 ( e9783110307290_i0441.jpg), 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 (e9783110307290_i0442.jpg). The same situation is true for stochastic processes: Brownian motion ...

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