rMM {smam}

Sampling from a Moving-Moving Process with 2 Embedded Brownian Motion

Description

A moving-moving process consists of two states: moving (large) and moving (small). The transition between the two states is modeled by an alternating renewal process, with exponentially distributed duration. An animal moves according to two Brownian motions with different volatility parameters.

Usage

rMM(time, lamM1, lamM2, sigma1, sigma2, s0, dim = 2)

Arguments

time

time points at which observations are to be simulated

lamM1

rate parameter of the exponential duration while moving1

lamM2

rate parameter of the exponential duration while moving2

sigma1

volatility parameter of the Brownian motion while moving1

sigma2

volatility parameter of the Brownian motion while moving2

s0

the state at time 0, must be one of "m1" or "m2", for moving1 and moving2, respectively

dim

(integer) dimension of the Brownian motion

Value

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

References

Yan, J., Chen, Y., Lawrence-Apfel, K., Ortega, I. M., Pozdnyakov, V., Williams, S., and Meyer, T. (2014) A moving-resting process with an embedded Brownian motion for animal movements. Population Ecology. 56(2): 401–415.

Pozdnyakov, V., Elbroch, L., Labarga, A., Meyer, T., and Yan, J. (2017) Discretely observed Brownian motion governed by telegraph process: estimation. Methodology and Computing in Applied Probability. doi:10.1007/s11009-017-9547-6.

Examples

tgrid <- seq(0, 100, length=100)

dat <- rMM(tgrid, 1, 0.1, 1, 0.1, "m1")
plot(dat[,1], dat[,2], xlab="t", ylab="X(t)", type='l')