In this article, we establish a connection between a stochastic dynamic model (SDM) driven by a linear stochastic differential equation (SDE) and a Chebyshev spline, which enables researchers to borrow strength across fields both theoretically and numerically. We construct a differential operator for the penalty function and develop a reproducing kernel Hilbert space (RKHS) induced by the SDM and the Chebyshev spline. The general form of the linear SDE allows us to extend the well‐known connection between an integrated Brownian motion and a polynomial spline to a connection between more complex diffusion processes and Chebyshev splines. One interesting special case is connection between an integrated Ornstein–Uhlenbeck process and an exponential spline. We use two real data sets to illustrate the integrated Ornstein–Uhlenbeck process model and exponential spline model and show their estimates are almost identical. The Canadian Journal of Statistics 42: 610–634; 2014 © 2014 Statistical Society of Canada

中文翻译：

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随机动力学模型和切比雪夫样条曲线。

在本文中，我们建立了由线性随机微分方程（SDE）驱动的随机动力学模型（SDM）与Chebyshev样条之间的联系，这使研究人员可以在理论上和数字上借用跨领域的实力。我们构造了罚函数的微分算子，并开发了由SDM和Chebyshev样条引起的再生内核希尔伯特空间（RKHS）。线性SDE的一般形式使我们能够将积分布朗运动与多项式样条之间的众所周知的连接扩展为更复杂的扩散过程与Chebyshev样条之间的连接。一个有趣的特殊情况是集成的Ornstein–Uhlenbeck过程与指数样条之间的联系。加拿大统计杂志42：610-634；加拿大统计局。2014©2014加拿大统计学会