datasim03: Simulated diffusion dataset 03

In mixediffusion: Mixed-Effects Diffusion Models with General Drift

Simulated diffusion dataset 03

Description

A simulated dataset consisting of discretely observed trajectories generated from a one-dimensional Ornstein–Uhlenbeck diffusion model with a time-dependent mean function and random effects.

Usage

data(datasim03)

Format

A data frame with observations from multiple experimental units and the following variables:

t

Observation time.

unit

Unit identifier.

Y

Observed process value.

Details

The data were generated from the stochastic differential equation

dY_k(t) = \lambda \{ a_k t - Y_k(t) \} \, dt + \sigma \, dW_k(t),

where the unit-specific random effects follow a normal distribution

a_k \sim \mathcal{N}(10, 3),

the mean-reversion parameter is given by \lambda = 0.75, and the diffusion variance satisfies \sigma^2 = 500.

The process was simulated for K = 30 units, each observed at n = 200 equally spaced time points over the interval [0, 10], with initial condition Y_k(0) = 0.

Value

A data frame with simulated data.

Source

Simulated data generated for illustrative purposes.

References

None.

Examples

data(datasim03)
plot_paths(df = datasim03)

mixediffusion documentation built on March 20, 2026, 5:10 p.m.