On the martingale property of stochastic exponentials

@article{Wong2004OnTM,
  title={On the martingale property of stochastic exponentials},
  author={Bernard Wong and Chris C. Heyde},
  journal={Journal of Applied Probability},
  year={2004},
  volume={41},
  pages={654 - 664}
}
We present a necessary and sufficient condition for a stochastic exponential to be a true martingale. It is proved that the criteria for the true martingale property are related to whether a related process explodes. An alternative and interesting interpretation of this result is that the stochastic exponential is a true martingale if and only if under a ‘candidate measure’ the integrand process is square integrable over time. Applications of our theorem to problems arising in mathematical… 

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