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and we now integrate from 0 to t:

jePsdW (s)

We have created a new kind of stochastic entity, an integral involving the increment of Brownian motion. Before we can understand the Ornstein-Uhlenbeck process, we need to understand that stochastic integral, so let us set

aePsdW (s)

Some properties of G(t) come to us for free: it is normally distributed and the mean E{G(t)} = 0. But what about the variance? In order to compute the variance of G(t), let us divide the interval [0, t] into pieces by picking a large number N and setting

1 NJ

so that we can approximate G(t) by a summation

0 0

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