Abstract
We investigate properties of processes X t which are weak solutions of multidimensional stochastic differential equations of the form dX t=b(t,X t) dt+ dW t. We show that under certain non-stochastic conditions the solution X t itself satisfies a uniform Novikov property. Consequently, it will follow that under these assumptions the no arbitrage property of X t can be obtained by applying the Girsanov theorem twice (in reverse directions). For the sake of illustration, some examples with exploding drifts b are presented.
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