# rTrajWn1D: Simulation of trajectories for the WN diffusion in 1D In sdetorus: Statistical Tools for Toroidal Diffusions

## Description

Simulation of the Wrapped Normal (WN) diffusion in 1D by subsampling a fine trajectory obtained by the Euler discretization.

## Usage

 ```1 2``` ```rTrajWn1D(x0, alpha, mu, sigma, N = 100, delta = 0.01, NFine = ceiling(N * delta/deltaFine), deltaFine = min(delta/100, 0.001)) ```

## Arguments

 `x0` initial point. `alpha` drift parameter. `mu` mean parameter. Must be in [π,π). `sigma` diffusion coefficient. `N` number of discretization steps in the resulting trajectory. `delta` discretization step. `NFine` number of discretization steps for the fine trajectory. Must be larger than `N`. `deltaFine` discretization step for the fine trajectory. Must be smaller than `delta`.

## Details

The fine trajectory is subsampled using the indexes `seq(1, NFine + 1, by = NFine / N)`.

## Value

A vector of length `N + 1` containing `x0` in the first entry and the discretized trajectory.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```isRStudio <- identical(.Platform\$GUI, "RStudio") if (isRStudio) { manipulate::manipulate({ x <- seq(0, N * delta, by = delta) plot(x, x, ylim = c(-pi, pi), type = "n", ylab = expression(X[t]), xlab = "t") linesCirc(x, rTrajWn1D(x0 = 0, alpha = alpha, mu = 0, sigma = sigma, N = N, delta = 0.01)) }, delta = slider(0.01, 5.01, step = 0.1), N = manipulate::slider(10, 500, step = 10, initial = 200), alpha = manipulate::slider(0.01, 5, step = 0.1, initial = 1), sigma = manipulate::slider(0.01, 5, step = 0.1, initial = 1)) } ```

sdetorus documentation built on Aug. 19, 2021, 9:06 a.m.