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Theory of Probability and Mathematical Statistics



STOCHASTIC DIFFERENTIAL EQUATIONS WITH GENERALIZED STOCHASTIC VOLATILITY AND STATISTICAL ESTIMATORS

M. BEL HADJ KHLIFA, YU. MISHURA, K. RALCHENKO, G. SHEVCHENKO, M. ZILI

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Abstract: We study a stochastic di erential equation, the di usion coecient of which is a function of some adapted stochastic process. The various conditions for the existence and uniqueness of weak and strong solutions are presented. The drift parameter estimation in this model is investigated, and the strong consistency of the least squares and maximum likelihood estimators is proved. As an example, the Ornstein{Uhlenbeck model with stochastic volatility is considered.

Keywords: Stochastic di erential equation, weak and strong solutions, stochastic volatility, drift parameter estimation, maximum likelihood estimator, strong consistency

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