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Vector-valued Generalised Ornstein-Uhlenbeck Processes by Voutilainen, Marko; Viitasaari, Lauri; Ilmonen, Pauliina; Torres, Soledad; Tudor, Ciprian is a scholarly article available to read on EtoBox.

What is Vector-valued Generalised Ornstein-Uhlenbeck Processes about?

Generalisations of the Ornstein-Uhlenbeck process defined through Langevin equation $dU_t = - \Theta U_t dt + dG_t,$ such as fractional Ornstein-Uhlenbeck processes, have recently received a lot of attention in the literature. In particular, estimation of the unknown parameter $\Theta$ is widely studied under Gaussian stationary increment noise $G$. Langevin equation is well-known for its connections to physics. In addition to that, motivation for studying Langevin equation with a general noise $G$ stems from the fact that the equation characterises all univariate stationary processes. Most of the literature on the topic focuses on the one-dimensional case with Gaussian noise $G$. In this article, we consider estimation of the unknown model parameter in the multidimensional version of the Langevin equation, where the parameter $\Theta$ is a matrix and $G$ is a general, not necessarily Gaussian, vector-valued process with stationary increments. Based on algebraic Riccati equations, we construct an estimator for the matrix $\Theta$. Moreover, we prove the consistency of the estimator and derive its limiting distribution under natural assumptions. In addition, to motivate our work, we

Author

Voutilainen, Marko; Viitasaari, Lauri; Ilmonen, Pauliina; Torres, Soledad; Tudor, Ciprian

Published

2019

Language

EN