共查询到20条相似文献,搜索用时 46 毫秒
1.
Statistical Inference for Stochastic Processes - We deal with the fractional Ornstein–Uhlenbeck (fO–U) process driven by the fractional Brownian motion (fBm), where the drift parameter... 相似文献
2.
B. L. S. Prakasa Rao 《随机分析与应用》2017,35(6):943-953
We investigate the asymptotic properties of instrumental variable estimators of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by mixed fractional Brownian motion. 相似文献
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B. L. S. Prakasa Rao 《随机分析与应用》2013,31(6):1203-1215
Abstract We investigate the asymptotic properties of instrumental variable estimators of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by fractional Brownian motion. 相似文献
5.
B. L. S. Prakasa Rao 《随机分析与应用》2013,31(5):767-781
ABSTRACTWe investigate the asymptotic properties of the maximum likelihood estimator and Bayes estimator of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by a mixed fractional Brownian motion. We obtain a Bernstein–von Mises-type theorem also for such a class of processes. 相似文献
6.
We consider the fractional analogue of the Ornstein–Uhlenbeck process, that is, the solution of a one-dimensional homogeneous
linear stochastic differential equation driven by a fractional Brownian motion in place of the usual Brownian motion. The
statistical problem of estimation of the drift and variance parameters is investigated on the basis of a semimartingale which
generates the same filtration as the observed process. The asymptotic behaviour of the maximum likelihood estimator of the
drift parameter is analyzed. Strong consistency is proved and explicit formulas for the asymptotic bias and mean square error
are derived. Preparing for the analysis, a change of probability method is developed to compute the Laplace transform of a
quadratic functional of some auxiliary process.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
7.
本文研究混合分数O-U过程的最小范数估计问题.利用分数布朗运动驱动的随机微分方程偏差不等式,获得了混合分数O-U过程漂移参数的最小范数估计、相合性及渐近分布. 相似文献
8.
《随机分析与应用》2013,31(6):1487-1509
Abstract We apply Grenander's method of sieves to the problem of identification or estimation of the “drift” function for linear stochastic systems driven by a fractional Brownian motion (fBm). We use an increasing sequence of finite dimensional subspaces of the parameter space as the natural sieves on which we maximise the likelihood function. 相似文献
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We study a stochastic control system involving both a standard and a fractional Brownian motion with Hurst parameter less than 1/2. We apply an anticipative Girsanov transformation to transform the system into another one, driven only by the standard Brownian motion with coefficients depending on both the fractional Brownian motion and the standard Brownian motion. We derive a maximum principle and the associated stochastic variational inequality, which both are generalizations of the classical case. 相似文献
11.
Using the multiple stochastic integrals, we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one- and two-parameter cases. When the drift is zero, we show that in the one-parameter case the solution is an exponential—thus positive—function while in the two-parameter setting the solution is negative on a non-negligible set. 相似文献
12.
Hideaki Uemura 《随机分析与应用》2013,31(1):136-168
Abstract We determine the weighted local time for the multidimensional fractional Brownian motion from the occupation time formula. We also discuss on the Itô and Tanaka formula for the multidimensional fractional Brownian motion. In these formulas the Skorohod integral is applicable if the Hurst parameter of fractional Brownian motion is greater than 1/2. If the Hurst parameter is less than 1/2, then we use the Skorohod type integral introduced by Nualart and Zakai for the stochastic integral and establish the Itô and Tanaka formulas. 相似文献
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We construct fractional Brownian motion, sub-fractional Brownian motion and negative sub-fractional Brownian motion by means of limiting procedures applied to some particle systems. These processes are obtained for full ranges of Hurst parameter. 相似文献
14.
In this paper, we show the existence of a weak solution for a stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter , and a discontinuous drift. The proof of this result is based on the Girsanov theorem for the fractional Brownian motion. 相似文献
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《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(11):1067-1074
We show that geometric Brownian motion with parameter μ, i.e., the exponential of linear Brownian motion with drift μ, divided by its quadratic variation process is a diffusion process. Taking logarithms and an appropriate scaling limit, we recover the Rogers-Pitman extension to Brownian motion with drift of Pitman's representation theorem for the three-dimensional Bessel process. Time inversion and generalized inverse Gaussian distributions play crucial roles in our proofs. 相似文献
16.
In this note, we prove an existence and uniqueness result of solution for stochastic differential delay equations with hereditary
drift driven by a fractional Brownian motion with Hurst parameter H > 1/2. Then, we show that, when the delay goes to zero, the solutions to these equations converge, almost surely and in L
p
, to the solution for the equation without delay. The stochastic integral with respect to the fractional Brownian motion is
a pathwise Riemann–Stieltjes integral. 相似文献
17.
M. N. Mishra 《随机分析与应用》2016,34(4):707-721
We study the local asymptotic normality and estimation for drift parameter obtained through Kalman–Bucy filter for linear systems driven by fractional Brownian motions. 相似文献
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Ciprian A. Tudor Mounir Zili 《NoDEA : Nonlinear Differential Equations and Applications》2016,23(5):53
We consider a stochastic partial differential equation involving a second order differential operator whose drift is discontinuous. The equation is driven by a Gaussian noise which behaves as a Wiener process in space and the time covariance generates a signed measure. This class includes the Brownian motion, fractional Brownian motion and other related processes. We give a necessary and sufficient condition for the existence of the solution and we study the path regularity of this solution. 相似文献
19.
Jean-Christophe Breton Jean-Fran?ois Coeurjolly 《Statistical Inference for Stochastic Processes》2012,15(1):1-26
In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose confidence intervals
of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the fractional Brownian
motion is known or unknown are investigated. These intervals are obtained by observing a single discretized sample path of
a fractional Brownian motion and without any assumption on the Hurst parameter H. 相似文献
20.
Jiro Akahori Xiaoming Song Tai-Ho Wang 《Stochastic Processes and their Applications》2019,129(1):174-204
The article shows a bridge representation for the joint density of a system of stochastic processes consisting of a Brownian motion with drift coupled with a correlated fractional Brownian motion with drift. As a result, a small time approximation of the joint density is readily obtained by substituting the conditional expectation under the bridge measure by a single path: the modal-path from the initial point to the terminal point. 相似文献