Sample from a simulated Ornstein-Uhlenbeck process with time-dependent mean

The data was simulated using a standard Euler-Maruyama method.

The simulated process is governed by the SDE #' dx ~ theta * (mu + u - x) * dt + sigma_x * dw

The parameters used for simulation were theta = 5, mu = 3, sigma_x = 1, sigma_y = 0.1

The simulation time-step was 1e-3, and observation time-step 1e-1. The simulation was taken from t = 0..20

The simulated input was given by u.sim = cumsum(rnorm(length(t.sim),sd=0.05)) where t.sim is the simulated time vector.

Usage

Ornstein

Format

A data frame of 201 rows and 3 columns. The columns represent the variables: t (time), y (observation) and u (input).