多维积分分数阶奥恩斯坦-乌伦贝克过程及其在动物运动中的应用
Multidimensional Integral Fractional Ornstein--Uhlenbeck Process with an Application to Animal Movement
AI总结：
本文将积分分数阶奥恩斯坦-乌伦贝克（ifOU）过程扩展为多维模型，用于动物遥测，建立了协方差有效性等理论结果并开发了模拟、推断等方法，经模拟验证后应用于德国夜蝠的运动遥测数据。
AI中文摘要：
分数阶奥恩斯坦-乌伦贝克（fOU）过程可建模时间依赖性与记忆性，包括长程依赖性，同时保留经典奥恩斯坦-乌伦贝克过程作为特例。我们将积分分数阶奥恩斯坦-乌伦贝克（ifOU）过程扩展至适用于动物遥测的多维场景，经度、纬度和高度速度由坐标特异性fOU过程表示，该过程由多元分数布朗运动驱动，允许每个坐标保留自身的阻尼、尺度和赫斯特参数。我们建立了协方差有效性，刻画了可容许互相关区域，并推导了互协方差与分离增量的渐近行为。我们开发了有限维模拟、高斯似然推断及条件速度重构的方法。重复模拟用于检验跨坐标相关性的估计，同时针对一条三维轨迹演示了完整参数向量的联合估计。所提模型应用于德国迁徙的五只普通夜蝠的遥测记录，其中包括三条带有高度测量的轨迹。
英文摘要：
Fractional Ornstein--Uhlenbeck (fOU) processes model temporal dependence and memory, including long-range dependence, while retaining the classical Ornstein--Uhlenbeck process as a special case. We extend the integral fractional Ornstein--Uhlenbeck (ifOU) process to a multidimensional setting for animal telemetry. Longitude, Latitude, and Altitude velocities are represented by coordinate-specific fOU processes driven by a multivariate fractional Brownian motion, allowing each coordinate to retain its own damping, scale, and Hurst parameters. We establish covariance validity, characterize the admissible cross-correlation region, and derive the asymptotic behavior of cross-covariances and separated increments. We develop procedures for finite-dimensional simulation, Gaussian likelihood inference, and conditional velocity reconstruction. Replicated simulations examine estimation of cross-coordinate correlations, while joint estimation of the complete parameter vector is illustrated for one three-dimensional trajectory. The proposed model is applied to telemetry records from five common noctule bats migrating in Germany, including three trajectories with Altitude measurements.
