The Experts below are selected from a list of 11151 Experts worldwide ranked by ideXlab platform

Yuliya Mishura - One of the best experts on this subject based on the ideXlab platform.

  • time changed fractional Ornstein Uhlenbeck Process
    Fractional Calculus and Applied Analysis, 2020
    Co-Authors: Giacomo Ascione, Yuliya Mishura, Enrica Pirozzi
    Abstract:

    We define a time-changed fractional Ornstein-Uhlenbeck Process by composing a fractional Ornstein-Uhlenbeck Process with the inverse of a subordinator. Properties of the moments of such Process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the Process.

  • Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications
    Methodology and Computing in Applied Probability, 2019
    Co-Authors: Giacomo Ascione, Yuliya Mishura, Enrica Pirozzi
    Abstract:

    We consider a fractional Ornstein-Uhlenbeck Process involving a stochastic forcing term in the drift, as a solution of a linear stochastic differential equation driven by a fractional Brownian motion. For such Process we specify mean and covariance functions, concentrating on their asymptotic behavior. This gives us a sort of short- or long-range dependence, under specified hypotheses on the covariance of the forcing Process. Applications of this Process in neuronal modeling are discussed, providing an example of a stochastic forcing term as a linear combination of Heaviside functions with random center. Simulation algorithms for the sample path of this Process are given.

  • hypothesis testing of the drift parameter sign for fractional Ornstein Uhlenbeck Process
    Electronic Journal of Statistics, 2017
    Co-Authors: Alexander Kukush, Yuliya Mishura, Kostiantyn Ralchenko
    Abstract:

    We consider the fractional Ornstein–Uhlenbeck Process with an unknown drift parameter and known Hurst parameter $H$. We propose a new method to test the hypothesis of the sign of the parameter and prove the consistency of the test. Contrary to the previous works, our approach is applicable for all $H\in(0,1)$.

  • Hypothesis testing of the drift parameter sign for fractional Ornstein-Uhlenbeck Process
    arXiv: Probability, 2016
    Co-Authors: Alexander Kukush, Yuliya Mishura, Kostiantyn Ralchenko
    Abstract:

    We consider the fractional Ornstein-Uhlenbeck Process with an unknown drift parameter and known Hurst parameter $H$. We propose a new method to test the hypothesis of the sign of the parameter and prove the consistency of the test. Contrary to the previous works, our approach is applicable for all $H\in(0,1)$. We also study the estimators for drift parameter for continuous and discrete observations and prove their strong consistency for all $H\in(0,1)$.

  • option pricing in the model with stochastic volatility driven by Ornstein Uhlenbeck Process simulation
    Research Papers in Economics, 2016
    Co-Authors: Sergii Kuchukiatsenko, Yuliya Mishura
    Abstract:

    We consider a discrete-time approximation of paths of an Ornstein--Uhlenbeck Process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler--Maruyama approximation scheme is implemented. We determine the estimates for the option price for predetermined sets of parameters. The rate of convergence of the price and an average volatility when discretization intervals tighten are determined. Discretization precision is analyzed for the case where the exact value of the price can be derived.

Enrica Pirozzi - One of the best experts on this subject based on the ideXlab platform.

  • time changed fractional Ornstein Uhlenbeck Process
    Fractional Calculus and Applied Analysis, 2020
    Co-Authors: Giacomo Ascione, Yuliya Mishura, Enrica Pirozzi
    Abstract:

    We define a time-changed fractional Ornstein-Uhlenbeck Process by composing a fractional Ornstein-Uhlenbeck Process with the inverse of a subordinator. Properties of the moments of such Process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the Process.

  • Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications
    Methodology and Computing in Applied Probability, 2019
    Co-Authors: Giacomo Ascione, Yuliya Mishura, Enrica Pirozzi
    Abstract:

    We consider a fractional Ornstein-Uhlenbeck Process involving a stochastic forcing term in the drift, as a solution of a linear stochastic differential equation driven by a fractional Brownian motion. For such Process we specify mean and covariance functions, concentrating on their asymptotic behavior. This gives us a sort of short- or long-range dependence, under specified hypotheses on the covariance of the forcing Process. Applications of this Process in neuronal modeling are discussed, providing an example of a stochastic forcing term as a linear combination of Heaviside functions with random center. Simulation algorithms for the sample path of this Process are given.

Bernard Bercu - One of the best experts on this subject based on the ideXlab platform.

  • large deviations for the Ornstein Uhlenbeck Process without tears
    Statistics & Probability Letters, 2017
    Co-Authors: Bernard Bercu, Adrien Richou
    Abstract:

    Abstract Our goal is to establish large deviations for the maximum likelihood estimator of the drift parameter of the Ornstein–Uhlenbeck Process without tears. We propose a new strategy to establish large deviation results which allows us, via a suitable transformation, to circumvent the classical difficulty of non-steepness. Our approach holds in the stable case where the Process is positive recurrent as well as in the unstable and explosive cases where the Process is respectively null recurrent and transient. It can also be successfully implemented for more complex diffusion Processes.

  • large deviations for the Ornstein Uhlenbeck Process without tears
    2016
    Co-Authors: Bernard Bercu, Adrien Richou
    Abstract:

    Our goal is to establish large deviations and concentration inequalities for the maximum likelihood estimator of the drift parameter of the Ornstein-Uhlenbeck Process without tears. We propose a new strategy to establish large deviation results which allows us, via a suitable transformation, to circumvent the classical difficulty of non-steepness. Our approach holds in the stable case where the Process is positive recurrent as well as in the unstable and explosive cases where the Process is respectively null recurrent and transient. Notwithstanding of this trichotomy, we also provide new concentration inequalities for the maximum likelihood estimator.

  • large deviations for the Ornstein Uhlenbeck Process with shift
    Advances in Applied Probability, 2015
    Co-Authors: Bernard Bercu, Adrien Richou
    Abstract:

    We investigate the large deviation properties of the maximum likelihood estimators for the Ornstein-Uhlenbeck Process with shift. We estimate simultaneously the drift and shift parameters. On the one hand, we establish a large deviation principle for the maximum likelihood estimates of the drift and shift parameters. Surprisingly, we find that the drift estimator shares the same large deviation principle as the one previously established for the Ornstein-Uhlenbeck Process without shift. Sharp large deviation principles are also provided. On the other hand, we show that the maximum likelihood estimator of the shift parameter satisfies a large deviation principle with a very unusual implicit rate function.

  • Sharp large deviations for the non-stationary Ornstein-Uhlenbeck Process
    Stochastic Processes and their Applications, 2012
    Co-Authors: Bernard Bercu, Laure Coutin, Nicolas Savy
    Abstract:

    For the Ornstein-Uhlenbeck Process, the asymptotic behavior of the maximum likelihood estimator of the drift parameter is totally different in the stable, unstable, and explosive cases. Notwithstanding of this trichotomy, we investigate sharp large deviation principles for this estimator in the three situations. In the explosive case, we exhibit a very unusual rate function with a shaped flat valley and an abrupt discontinuity point at its minimum.

  • Sharp large deviations for the fractional Ornstein-Uhlenbeck Process
    SIAM Theory of Probability and its Applications, 2011
    Co-Authors: Bernard Bercu, Laure Coutin, Nicolas Savy
    Abstract:

    We investigate the sharp large deviation properties of the energy and the maximum likelihood estimator for the Ornstein-Uhlenbeck Process driven by a fractional Brownian motion with Hurst index greater than one half.

Giacomo Ascione - One of the best experts on this subject based on the ideXlab platform.

  • time changed fractional Ornstein Uhlenbeck Process
    Fractional Calculus and Applied Analysis, 2020
    Co-Authors: Giacomo Ascione, Yuliya Mishura, Enrica Pirozzi
    Abstract:

    We define a time-changed fractional Ornstein-Uhlenbeck Process by composing a fractional Ornstein-Uhlenbeck Process with the inverse of a subordinator. Properties of the moments of such Process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the Process.

  • Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications
    Methodology and Computing in Applied Probability, 2019
    Co-Authors: Giacomo Ascione, Yuliya Mishura, Enrica Pirozzi
    Abstract:

    We consider a fractional Ornstein-Uhlenbeck Process involving a stochastic forcing term in the drift, as a solution of a linear stochastic differential equation driven by a fractional Brownian motion. For such Process we specify mean and covariance functions, concentrating on their asymptotic behavior. This gives us a sort of short- or long-range dependence, under specified hypotheses on the covariance of the forcing Process. Applications of this Process in neuronal modeling are discussed, providing an example of a stochastic forcing term as a linear combination of Heaviside functions with random center. Simulation algorithms for the sample path of this Process are given.

Cheyenne M Moreau - One of the best experts on this subject based on the ideXlab platform.

  • beyond brownian motion and the Ornstein Uhlenbeck Process stochastic diffusion models for the evolution of quantitative characters
    The American Naturalist, 2020
    Co-Authors: Simon P Blomberg, Suren I Rathnayake, Cheyenne M Moreau
    Abstract:

    Gaussian Processes, such as Brownian motion and the Ornstein-Uhlenbeck Process, have been popular models for the evolution of quantitative traits and are widely used in phylogenetic comparative methods. However, they have drawbacks that limit their utility. Here we describe new, non-Gaussian stochastic differential equation (diffusion) models of quantitative trait evolution. We present general methods for deriving new diffusion models and develop new software for fitting non-Gaussian evolutionary models to trait data. The theory of stochastic Processes provides a mathematical framework for understanding the properties of current and future phylogenetic comparative methods. Attention to the mathematical details of models of trait evolution and diversification may help avoid some pitfalls when using stochastic Processes to model macroevolution.