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Statistical aspects of the fractional stochastic calculus
15 references·15 citing·34 second hop
Statistical aspects of the fractional stochastic calculus (2007)Statistical aspects of the fractional sto…FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE (2003)FRACTIONAL WHITE NOISE CALCUL…Fractional Ornstein-Uhlenbeck processes (2003)Fractional Ornstein-Uhlenbeck…Statistical Analysis of the Fractional Ornstein–Uhlenbeck Type Process (2002)Statistical Analysis of the F…Regularization of differential equations by fractional noise (2002)Regularization of differentia…Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach (2002)Maximum Likelihood Estimation…Stochastic Calculus with Respect to Gaussian Processes (2001)Stochastic Calculus with Resp…Stochastic Analysis of the Fractional Brownian Motion (1999)Stochastic Analysis of the Fr…Statistical inference for diffusion type processes (1999)Statistical inference for dif…Continuous Martingales and Brownian Motion (1999)Continuous Martingales and Br…An Elementary Approach to a Girsanov Formula and Other Analytical Results on Fractional Brownian Motions (1999)An Elementary Approach to a G…The Malliavin Calculus and Related Topics (1995)The Malliavin Calculus and Re…Martingale Estimation Functions for Discretely Observed Diffusion Processes (1995)Martingale Estimation Functio…A New Approach to Maximum Likelihood Estimation for Stochastic Differential Equations Based on Discrete Observations (1993)A New Approach to Maximum Lik…Estimation of the coefficients of a diffusion from discrete observations (1986)Estimation of the coefficient…Stochastic calculus of variation and hypoelliptic operators (1978)Stochastic calculus of variat…Moderate Deviations for Parameter Estimation in the Fractional Ornstein-Uhlenbeck Processes with Periodic Mean (2023)Moderate Deviations for Param…Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process (2021)Modeling and forecasting real…Drift parameter estimation for nonlinear stochastic differential equations driven by fractional Brownian motion (2019)Drift parameter estimation fo…Statistical inference for Vasicek-type model driven by Hermite processes (2018)Statistical inference for Vas…Optimal rates for parameter estimation of stationary Gaussian processes (2018)Optimal rates for parameter e…ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL (2018)ASYMPTOTIC THEORY FOR ESTIMAT…Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter (2017)Parameter estimation for frac…Parameter estimation for a partially observed Ornstein–Uhlenbeck process with long-memory noise (2016)Parameter estimation for a pa…Least squares estimator for non-ergodic Ornstein–Uhlenbeck processes driven by Gaussian processes (2016)Least squares estimator for n…Quadratic variations for the fractional-colored stochastic heat equation (2014)Quadratic variations for the …Berry–Esséen bounds for the least squares estimator for discretely observed fractional Ornstein–Uhlenbeck processes (2013)Berry–Esséen bounds for the l…A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise (2013)A least square-type procedure…Maximum-likelihood estimators and random walks in long memory models (2010)Maximum-likelihood estimators…Drift parameter estimation in fractional diffusions driven by perturbed random walks (2010)Drift parameter estimation in…ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR FOR STOCHASTIC PARABOLIC EQUATIONS WITH ADDITIVE FRACTIONAL BROWNIAN MOTION (2009)ASYMPTOTIC PROPERTIES OF THE …Stochastic Integration and Differential Equations (1990)Analysis of the Rosenblatt process (2008)Out of sample forecasts of quadratic variation (2008)Parameter estimation for fractional Ornstein–Uhlenbeck processes (2010)Fractional Brownian Motions, Fractional Noises and Applications (1968)Stochastic Calculus for Fractional Brownian Motion I. 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References

  • 1999Continuous Martingales and Brownian Motion6,200 cited
  • 1995The Malliavin Calculus and Related Topics1,545 cited
  • 2002Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach902 cited
  • 1999Stochastic Analysis of the Fractional Brownian Motion744 cited
  • 2001Stochastic Calculus with Respect to Gaussian Processes536 cited
  • 2003FRACTIONAL WHITE NOISE CALCULUS AND APPLICATIONS TO FINANCE476 cited
  • 2003Fractional Ornstein-Uhlenbeck processes418 cited
  • 1999An Elementary Approach to a Girsanov Formula and Other Analytical Results on Fractional Brownian Motions401 cited
  • 1995Martingale Estimation Functions for Discretely Observed Diffusion Processes348 cited
  • 1999Statistical inference for diffusion type processes307 cited
  • 1993A New Approach to Maximum Likelihood Estimation for Stochastic Differential Equations Based on Discrete Observations269 cited
  • 2002Statistical Analysis of the Fractional Ornstein–Uhlenbeck Type Process267 cited
  • 1986Estimation of the coefficients of a diffusion from discrete observations245 cited
  • 1978Stochastic calculus of variation and hypoelliptic operators178 cited
  • 2002Regularization of differential equations by fractional noise

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170 cited

Cited by

  • 2017Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter125 cited
  • 2021Modeling and forecasting realized volatility with the fractional Ornstein–Uhlenbeck process80 cited
  • 2016Least squares estimator for non-ergodic Ornstein–Uhlenbeck processes driven by Gaussian processes75 cited
  • 2009ASYMPTOTIC PROPERTIES OF THE MAXIMUM LIKELIHOOD ESTIMATOR FOR STOCHASTIC PARABOLIC EQUATIONS WITH ADDITIVE FRACTIONAL BROWNIAN MOTION70 cited
  • 2018ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL62 cited
  • 2013A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise52 cited
  • 2018Optimal rates for parameter estimation of stationary Gaussian processes51 cited
  • 2016Parameter estimation for a partially observed Ornstein–Uhlenbeck process with long-memory noise47 cited
  • 2018Statistical inference for Vasicek-type model driven by Hermite processes44 cited
  • 2013Berry–Esséen bounds for the least squares estimator for discretely observed fractional Ornstein–Uhlenbeck processes39 cited
  • 2019Drift parameter estimation for nonlinear stochastic differential equations driven by fractional Brownian motion37 cited
  • 2023Moderate Deviations for Parameter Estimation in the Fractional Ornstein-Uhlenbeck Processes with Periodic Mean36 cited
  • 2010Drift parameter estimation in fractional diffusions driven by perturbed random walks35 cited
  • 2014Quadratic variations for the fractional-colored stochastic heat equation29 cited
  • 2010Maximum-likelihood estimators and random walks in long memory models29 cited