Novikov's condition

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Novikov's condition is sufficient for application of Girsanov's theorem to certain classes of stochastic processes. The Novikov condition.

\mathbf{E} \left [\exp\left ( \frac{1}{2} \int_{0}^{T} X^2_t\, dt \right )\right ] < \infty


Of particular interest is the class of exponential stochastic processes of the following form.

\ Z_t \ = \exp \left \lbrace \int_0^t X_s\, dW_s -\frac{1}{2}\int_0^t X_s^2\, ds \right \rbrace

Where Xt is an adapted process in the probabiity space \left (\Omega,\mathbb{P,}\mathbb{F}\right) and W is a Brownian Motion with respect to our probability measure \mathbb{P}.


If the condition is fulfilled then we can state that the process will be a martingale with respect to our filtration \mathbb{F} of the Brownian Motion and our probability measure \mathbb{P}.

[edit] External Link

Comments on Girsanov's Theorem by H. E. Krogstad, IMF 2003[1]

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