dTpdPde1D | R Documentation |
Computation of the transition probability density (tpd) of the Wrapped Normal (WN) or von Mises (vM) diffusion, by solving its associated Fokker–Planck Partial Differential Equation (PDE) in 1D.
dTpdPde1D(Mx = 500, x0, t, alpha, mu, sigma, type = "WN",
Mt = ceiling(100 * t), sdInitial = 0.1, ...)
Mx |
size of the equispaced spatial grid in |
x0 |
point giving the mean of the initial circular density, a WN with
standard deviation equal to |
t |
time separating |
alpha |
drift parameter. |
mu |
mean parameter. Must be in |
sigma |
diffusion coefficient. |
type |
either |
Mt |
size of the time grid in |
sdInitial |
the standard deviation of the concentrated WN giving the initial condition. |
... |
Further parameters passed to |
A combination of small sdInitial
and coarse space-time
discretization (small Mx
and Mt
) is prone to create numerical
instabilities. See Sections 3.4.1, 2.2.1 and 2.2.2 in García-Portugués et
al. (2019) for details.
A vector of length Mx
with the tpd evaluated at
seq(-pi, pi, l = Mx + 1)[-(Mx + 1)]
.
García-Portugués, E., Sørensen, M., Mardia, K. V. and Hamelryck, T. (2019) Langevin diffusions on the torus: estimation and applications. Statistics and Computing, 29(2):1–22. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11222-017-9790-2")}
Mx <- 100
x <- seq(-pi, pi, l = Mx + 1)[-c(Mx + 1)]
x0 <- pi
t <- 0.5
alpha <- 1
mu <- 0
sigma <- 1
isRStudio <- identical(.Platform$GUI, "RStudio")
if (isRStudio) {
manipulate::manipulate({
plot(x, dTpdPde1D(Mx = Mx, x0 = x0, t = t, alpha = alpha, mu = 0,
sigma = sigma), type = "l", ylab = "Density",
xlab = "", ylim = c(0, 0.75))
lines(x, dTpdWou1D(x = x, x0 = rep(x0, Mx), t = t, alpha = alpha, mu = 0,
sigma = sigma), col = 2)
}, x0 = manipulate::slider(-pi, pi, step = 0.01, initial = 0),
alpha = manipulate::slider(0.01, 5, step = 0.01, initial = 1),
sigma = manipulate::slider(0.01, 5, step = 0.01, initial = 1),
t = manipulate::slider(0.01, 5, step = 0.01, initial = 1))
}
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