# Multidimensional Integral Fractional Ornstein--Uhlenbeck Process with an Application to Animal Movement

arXiv: https://arxiv.org/abs/2608.03381 · HTML: https://mlsanity.com/paper/2608.03381/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2026.

## Built on by (most cited first, 1 of 1)

- [Inference for stochastic differential equations driven by weighted sub-fractional Brownian motion using neural networks and the Euler approximation](https://mlsanity.com/paper/2610.00793/) (2026)

## Abstract (arXiv)

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.