An uncoupled two-dimensional Ornstein-Uhlenbeck process simulated with affectOU.
Format
An object of class simulate_affectOU containing simulated trajectories from the specified Ornstein-Uhlenbeck process.
Details
The process is defined by the stochastic differential equation: $$d\mathbf{X}_t = \mathbf{\Theta}(\mathbf{\mu} - \mathbf{X}_t)dt + \mathbf{\Gamma}^{1/2}d\mathbf{W}_t$$
where:
\(\mathbf{\Theta} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\) is the drift matrix
\(\mathbf{\mu} = \begin{pmatrix} 0 \\ 0 \end{pmatrix}\) is the equilibrium mean vector
\(\mathbf{\Gamma} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}\) is the diffusion matrix
\(\mathbf{W}_t\) is a two-dimensional Wiener process