euler1D: Simulation of trajectories of the WN or vM diffusion in 1D

In sdetorus: Statistical Tools for Toroidal Diffusions

Simulation of trajectories of the WN or vM diffusion in 1D

Description

Simulation of the Wrapped Normal (WN) diffusion or von Mises (vM) diffusion by the Euler method in 1D, for several starting values.

Usage

euler1D(x0, alpha, mu, sigma, N = 100L, delta = 0.01, type = 1L,
  maxK = 2L, expTrc = 30)

Arguments

x0	vector of length nx0 giving the initial points.
alpha	drift parameter.
mu	mean parameter. Must be in [\pi,\pi).
sigma	diffusion coefficient.
N	number of discretization steps.
delta	discretization step.
type	integer giving the type of diffusion. Currently, only 1 for WN and 2 for vM are supported.
maxK	maximum absolute value of the windings considered in the computation of the WN.
expTrc	truncation for exponential: exp(x) with x <= -expTrc is set to zero. Defaults to 30.

Value

A matrix of size c(nx0, N + 1) containing the nx0 discretized trajectories. The first column corresponds to the vector x0.

Examples

N <- 100
nx0 <- 20
x0 <- seq(-pi, pi, l = nx0 + 1)[-(nx0 + 1)]
set.seed(12345678)
samp <- euler1D(x0 = x0, mu = 0, alpha = 3, sigma = 1, N = N,
                delta = 0.01, type = 2)
tt <- seq(0, 1, l = N + 1)
plot(rep(0, nx0), x0, pch = 16, col = rainbow(nx0), xlim = c(0, 1))
for (i in 1:nx0) linesCirc(tt, samp[i, ], col = rainbow(nx0)[i])

sdetorus documentation built on Aug. 21, 2023, 1:08 a.m.