Statistical estimation of the Oscillating Brownian Motion

@inproceedings{Lejay2017StatisticalEO,
  title={Statistical estimation of the Oscillating Brownian Motion},
  author={Antoine Lejay and Paolo Pigato},
  year={2017}
}
  • Antoine Lejay, Paolo Pigato
  • Published 2017
  • Mathematics
  • We study the asymptotic behavior of estimators of a two-valued, discontinuous diffusion coefficient in a Stochastic Differential Equation, called an Oscillating Brownian Motion. Using the relation of the latter process with the Skew Brownian Motion, we propose two natural consistent estimators, which are variants of the integrated volatility estimator and take the occupation times into account. We show the stable convergence of the renormalized errors' estimations toward some Gaussian mixture… CONTINUE READING

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