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Problems and Solutions in Mathematical Finance: Stochastic Calculus, Volume I by Eric Chin, Sverrir Olafsson, Dian Nel

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  1. 10. Ornstein–Uhlenbeck Process. Let c03-math-555 be a probability space and let c03-math-556 be a standard Wiener process. Suppose c03-math-557 follows the Ornstein–Uhlenbeck process with SDE
    equation

    where c03-math-558, c03-math-559 and c03-math-560 are constants. By applying Itō's formula to c03-math-561 and taking integrals show that for c03-math-562,

    equation

    Using the properties of stochastic integrals on the above expression, find the mean and variance of c03-math-563, given .

    Deduce that follows a normal distribution. ...

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