rBMME function

Sampling from Brown Motion with Measurement Error

Given the volatility parameters of a Brownian motion and normally distributed measurement errors, generate the process at discretely observed time points of a given dimension.

rBMME(time, dim = 2, sigma = 1, delta = 1)

rBmme(time, dim = 2, sigma = 1, delta = 1)

Arguments

• time: vector of time points at which observations are to be sampled
• dim: (integer) dimension of the Brownian motion
• sigma: volatility parameter (sd) of the Brownian motion
• delta: sd parameter of measurement error

Returns

A data.frame whose first column is the time points and whose other columns are coordinates of the locations.

Examples

tgrid <- seq(0, 10, length = 1001)
## make it irregularly spaced
tgrid <- sort(sample(tgrid, 800))
dat <- rBMME(tgrid, 1, 1)
plot(dat[,1], dat[,2], xlab="t", ylab="X(t)", type="l")

References

Pozdnyakov V., Meyer, TH., Wang, Y., and Yan, J. (2013) On modeling animal movements using Brownian motion with measurement error. Ecology 95(2): p247--253. doi:doi:10.1890/13-0532.1.