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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. 11. Multi-Dimensional Novikov Condition. Let c04-math-581 be an c04-math-582-dimensional c04-math-583-standard Wiener process, with c04-math-584, c04-math-585 an independent one-dimensional c04-math-586-standard Wiener process on the probability space c04-math-587. Suppose we have an c04-math-588-dimensional adapted process c04-math-589, c04-math-590. By considering
    equation

    and if

    equation

    where

    show that is a positive -martingale. ...

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