Maximum likelihood drift estimation for a threshold diffusion

Abstract : We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold diffusion is called the drifted Oscillating Brownian motion. The asymptotic behaviors of the positive and negative occupation times rule the ones of the estimators. Differently from most known results in the literature, we do not restrict ourselves to the ergodic framework: indeed, depending on the signs of the drift, the process may be ergodic, transient or null recurrent. For each regime, we establish whether or not the estimators are consistent; if they are, we prove the convergence in long time of the properly rescaled difference of the estimators towards a normal or mixed normal distribution. These theoretical results are backed by numerical simulations.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.inria.fr/hal-01731566
Contributeur : Antoine Lejay <>
Soumis le : mercredi 14 mars 2018 - 12:44:16
Dernière modification le : mercredi 10 octobre 2018 - 10:09:57
Document(s) archivé(s) le : vendredi 15 juin 2018 - 14:27:34

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estimation_drift_obm.pdf
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  • HAL Id : hal-01731566, version 1
  • ARXIV : 1803.05408

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Antoine Lejay, Paolo Pigato. Maximum likelihood drift estimation for a threshold diffusion. 2018. 〈hal-01731566〉

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