Problems and Solutions in Mathematical Finance: Stochastic Calculus, Volume I

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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

and if

where

show that is a positive -martingale. ...

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