datasim02: Simulated diffusion dataset 02

In mixediffusion: Mixed-Effects Diffusion Models with General Drift

Simulated diffusion dataset 02

Description

A simulated dataset consisting of discretely observed trajectories generated from a one-dimensional Wiener diffusion model with random effects in the drift term.

Usage

data(datasim02)

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) = a_k \sin(\pi t)\,dt + \sigma\,dW_k(t),

where the unit-specific random effects follow a normal distribution

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

and the diffusion variance is given by \sigma^2 = 50.

The integrated drift used for simulation is given by

\mu_{\Delta}(a_k, t_i, t_{i-1}) = \frac{a_k}{\pi} \left\{ \cos(\pi t_{i-1}) - \cos(\pi t_i) \right\}.

The process was simulated for K = 50 units, each observed at n = 200 equally spaced time points, with initial condition Y_{k0} = 1.

Value

A data frame with simulated data.

Source

Simulated data generated for illustrative purposes.

References

None.

Examples

data(datasim02)
plot_paths(df = datasim02)

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