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5. Stochastic integrals
We have seen that Brownian motion is infinitely variable, so we cannot define a Stieltjes integral associated with it. However, we shall see that it is possible to define an integral of another kind, defined in a quadratic sense.
5.1 Quadratic variation
Let X be a real-valued process. The following process is called the "approximate quadratic variation" of X at level n:
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Stochastic integrals
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