论文标题
带有随机强迫及其应用的分数Ornstein-Uhlenbeck过程
Fractional Ornstein-Uhlenbeck process with stochastic forcing and its applications
论文作者
论文摘要
我们将涉及随机强迫术语的分数Ornstein-uhlenbeck过程视为由分数Brownian运动驱动的线性随机微分方程的解决方案。对于这样的过程，我们指定平均值和协方差函数，专注于它们的渐近行为。这为我们提供了一种关于强迫过程协方差的指定假设的短期或长期依赖性。讨论了此过程在神经元建模中的应用，提供了一个随机强迫术语作为随机函数与随机中心的线性组合的示例。最终给出了此过程样本路径的仿真算法。
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 finally given.
