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Register a new userA Note On Inference for the Mixed Fractional Ornstein-Uhlenbeck Process with Drift
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This paper is devoted to parameter estimation of the mixed fractional Ornstein-Uhlenbeck process with a drift. Large sample asymptotical properties of the Maximum Likelihood Estimator is deduced using the Laplace transform computations or the Cameron-Martin formula with extra part from cite{CK19}
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In this paper, we will first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk. In order to verify the rationality of this simulation, we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein-Uhlenbeck process, and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter $H>1/2$.
This paper addresses the problem of estimating drift parameter of the Ornstein - Uhlenbeck type process, driven by the sum of independent standard and fractional Brownian motions. The maximum likelihood estimator is shown to be consistent and asymptotically normal in the large-sample limit, using some recent results on the canonical representation and spectral structure of mixed processes.
In this paper we consider the drift estimation problem for a general differential equation driven by an additive multidimensional fractional Brownian motion, under ergodic assumptions on the drift coefficient. Our estimation procedure is based on the identification of the invariant measure, and we provide consistency results as well as some information about the convergence rate. We also give some examples of coefficients for which the identifiability assumption for the invariant measure is satisfied.
We study normal diffusive and subdiffusive processes in a harmonic potential (Ornstein-Uhlenbeck process) on a uniformly growing/contracting domain. Our starting point is a recently derived fractional Fokker-Planck equation, which covers both the case of Brownian diffusion and the case of a subdiffusive Continuous-Time Random Walk (CTRW). We find a high sensitivity of the random walk properties to the details of the domain growth rate, which gives rise to a variety of regimes with extremely different behaviors. At the origin of this rich phenomenology is the fact that the walkers still move while they wait to jump, since they are dragged by the deterministic drift arising from the domain growth. Thus, the increasingly long waiting times associated with the ageing of the subdiffusive CTRW imply that, in the time interval between two consecutive jumps, the walkers might travel over much longer distances than in the normal diffusive case. This gives rise to seemingly counterintuitive effects. For example, on a static domain, both Brownian diffusion and subdiffusive CTRWs yield a stationary particle distribution with finite width when a harmonic potential is at play, thus indicating a confinement of the diffusing particle. However, for a sufficiently fast growing/contracting domain, this qualitative behavior breaks down, and differences between the Brownian case and the subdiffusive case are found. In the case of Brownian particles, a sufficiently fast exponential domain growth is needed to break the confinement induced by the harmonic force; in contrast, for subdiffusive particles such a breakdown may already take place for a sufficiently fast power-law domain growth. Our analytic and numerical results for both types of diffusion are fully confirmed by random walk simulations.
We calculate the two-point correlation function <x(t2)x(t1)> for a subdiffusive continuous time random walk in a parabolic potential, generalizing well-known results for the single-time statistics to two times. A closed analytical expression is found for initial equilibrium, revealing a clear deviation from a Mittag-Leffler decay.
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