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Enrica Pirozzi - One of the best experts on this subject based on the ideXlab platform.
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time changed fractional ornstein Uhlenbeck process
Fractional Calculus and Applied Analysis, 2020Co-Authors: Giacomo Ascione, Yuliya Mishura, Enrica PirozziAbstract: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.
Yuliya Mishura - One of the best experts on this subject based on the ideXlab platform.
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time changed fractional ornstein Uhlenbeck process
Fractional Calculus and Applied Analysis, 2020Co-Authors: Giacomo Ascione, Yuliya Mishura, Enrica PirozziAbstract: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.
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stochastic representation and pathwise properties of fractional cox ingersoll ross process
arXiv: Probability, 2017Co-Authors: Yuliya Mishura, Kostiantyn Ralchenko, V I Piterbarg, Anton YurchenkotytarenkoAbstract:We consider the fractional Cox-Ingersoll-Ross process satisfying the stochastic differential equation (SDE) $dX_t = aX_t\,dt + \sigma \sqrt{X_t}\,dB^H_t$ driven by a fractional Brownian motion (fBm) with Hurst parameter exceeding $\frac{2}{3}$. The integral $\int_0^t\sqrt{X_s}dB^H_s$ is considered as a pathwise integral and is equal to the limit of Riemann-Stieltjes integral sums. It is shown that the fractional Cox-Ingersoll-Ross process is a square of the fractional Ornstein-Uhlenbeck process until the first zero hitting. Based on that, we consider the square of the fractional Ornstein-Uhlenbeck process with an arbitrary Hurst index and prove that until its first zero hitting it satisfies the specified SDE if the integral $\int_0^t\sqrt{X_s}\,dB^H_s$ is defined as a pathwise Stratonovich integral. Therefore, the question about the first zero hitting time of the Cox-Ingersoll-Ross process, which matches the first zero hitting moment of the fractional Ornstein-Uhlenbeck process, is natural. Since the latter is a Gaussian process, it is proved by the estimates for distributions of Gaussian processes that for $a 0$ it is positive but less than 1. The upper bound for this probability is given.
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consistency of the drift parameter estimator for the discretized fractional ornstein Uhlenbeck process with hurst index h 0 12
Electronic Journal of Statistics, 2015Co-Authors: Kestutis Kubilius, Yuliya Mishura, Kostiantyn Ralchenko, Oleg SeleznjevAbstract:parameter θ and where the noise is modeled as fractional Brownian motionwith Hurst index H ∈ (0, 12 ). The solution corresponds to the fractionalOrnstein–Uhlenbeck process. We construct an estimato ...
Giacomo Ascione - One of the best experts on this subject based on the ideXlab platform.
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time changed fractional ornstein Uhlenbeck process
Fractional Calculus and Applied Analysis, 2020Co-Authors: Giacomo Ascione, Yuliya Mishura, Enrica PirozziAbstract: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.
Jorguwe Lobus - One of the best experts on this subject based on the ideXlab platform.
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infinite dimensional ornstein Uhlenbeck processes with unbounded diffusion approximation quadratic variation and ito formula
Mathematische Nachrichten, 2016Co-Authors: John Karlsson, Jorguwe LobusAbstract:This thesis consists of two papers which focuses on a particular diffusion type Dirichlet form where Here is the basis in the Cameron-Martin space, H, consisting of the Schauder functions, and ν denotes the Wiener measure.In Paper I, we let vary over the space of wiener trajectories in a way that the diffusion operator A is almost everywhere an unbounded operator on the Cameron–Martin space. In addition we put a weight function on theWiener measure and show that under these changes of the reference measure, the Malliavin derivative and divergence are closable operators with certain closable inverses. It is then shown that under certain conditions on , and these changes of reference measure, the Dirichlet form is quasi-regular. This is done first in the classical Wiener space and then the results are transferred to the Wiener space over a Riemannian manifold.Paper II focuses on the case when is a sequence of non-decreasing real numbers. The process X associated to is then an infinite dimensional Ornstein-Uhlenbeck process. In this case we show that the distributions of a sequence of certain finite dimensional Ornstein-Uhlenbeck processes converge weakly to the distribution of the infinite dimensional Ornstein-Uhlenbeck process. We also investigate the quadratic variation for this process, both in the classical sense and in the recent framework of stochastic calculus via regularization. Since the process is Banach space valued, the tensor quadratic variation is an appropriate tool to establish the Ito formula for the infinite dimensional Ornstein-Uhlenbeck process X. Sufficient conditions are presented for the scalar as well as the tensor quadratic variation to exist.
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infinite dimensional ornstein Uhlenbeck processes with unbounded diffusion approximation quadratic variation and it o formula
arXiv: Probability, 2015Co-Authors: John Karlsson, Jorguwe LobusAbstract:The paper studies a class of Ornstein-Uhlenbeck processes on the classical Wiener space. These processes are associated with a diffusion type Dirichlet form whose corresponding diffusion operator is unbounded in the Cameron-Martin space. It is shown that the distributions of certain finite dimensional Ornstein-Uhlenbeck processes converge weakly to the distribution of such an infinite dimensional Ornstein-Uhlenbeck process. For the infinite dimensional processes, the ordinary scalar quadratic variation is calculated. Moreover, relative to the stochastic calculus via regularization, the scalar as well as the tensor quadratic variation are derived. A related It\^o formula is presented.
Piotr Miloś - One of the best experts on this subject based on the ideXlab platform.
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u statistics of ornstein Uhlenbeck branching particle system
Journal of Theoretical Probability, 2014Co-Authors: Radoslaw Adamczak, Piotr MilośAbstract:We consider a branching particle system consisting of particles moving according to the Ornstein–Uhlenbeck process in $$\mathbb {R}^d$$ and undergoing a binary, supercritical branching with a constant rate $$\lambda >0$$ . This system is known to fulfill a law of large numbers (under exponential scaling). Recently the question of the corresponding central limit theorem (CLT) has been addressed. It turns out that the normalization and the form of the limit in the CLT fall into three qualitatively different regimes, depending on the relation between the branching intensity and the parameters of the Ornstein–Uhlenbeck process. In the present paper, we extend those results to $$U$$ -statistics of the system, proving a law of large numbers and CLT.
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u statistics of ornstein Uhlenbeck branching particle system
arXiv: Probability, 2011Co-Authors: Radoslaw Adamczak, Piotr MilośAbstract:We consider a branching particle system consisting of particles moving according to the Ornstein-Uhlenbeck process in $\Rd$ and undergoing a binary, supercritical branching with a constant rate $\lambda>0$. This system is known to fulfil a law of large numbers (under exponential scaling). Recently the question of the corresponding central limit theorem has been addressed. It turns out that the normalization and form of the limit in the CLT fall into three qualitatively different regimes, depending on the relation between the branching intensity and the parameters of the Orstein-Uhlenbeck process. In the present paper we extend those results to $U$-statistics of the system proving a law of large numbers and a central limit theorem.