Simulation of an Arithmetic Brownian Motion
This function simulates an Arithmetic Brownian Motion.
simm.mba(date = 1:100, x0 = c(0, 0), mu = c(0, 0),
sigma = diag(2), id = "A1", burst = id,
proj4string=CRS())date |
a vector indicating the date (in seconds) at which
relocations should be simulated. This vector can be of class
|
x0 |
a vector of length 2 containing the coordinates of the startpoint of the trajectory |
mu |
a vector of length 2 describing the drift of the movement |
sigma |
a 2*2 positive definite matrix |
id |
a character string indicating the identity of the simulated
animal (see |
burst |
a character string indicating the identity of the simulated
burst (see |
proj4string |
a valid CRS object containing the projection
information (see |
The arithmetic Brownian motion (Brillinger et al. 2002) can be described by the stochastic differential equation:
dz = mu * dt + Sigma dB2(t)
Coordinates of the animal at time t are contained in the vector
z(t). dz = c(dx, dy) is the increment of the
movement during dt. dB2(t) is a bivariate brownian Motion (see
?simm.brown). The vector mu measures the drift of the
motion. The matrix Sigma controls for perturbations due to the
random noise modeled by the Brownian motion. It can also be used to
take into account a potential correlation between the components dx
and dy of the animal moves during dt (see Examples).
An object of class ltraj
Clement Calenge clement.calenge@ofb.gouv.fr
Stephane Dray dray@biomserv.univ-lyon1.fr
Manuela Royer royer@biomserv.univ-lyon1.fr
Daniel Chessel chessel@biomserv.univ-lyon1.fr
Brillinger, D.R., Preisler, H.K., Ager, A.A. Kie, J.G. & Stewart, B.S. (2002) Employing stochastic differential equations to model wildlife motion. Bulletin of the Brazilian Mathematical Society 33: 385–408.
suppressWarnings(RNGversion("3.5.0"))
set.seed(253)
u <- simm.mba(1:1000, sigma = diag(c(4,4)),
burst = "Brownian motion")
v <- simm.mba(1:1000, sigma = matrix(c(2,-0.8,-0.8,2), ncol = 2),
burst = "cov(x,y) > 0")
w <- simm.mba(1:1000, mu = c(0.1,0), burst = "drift > 0")
x <- simm.mba(1:1000, mu = c(0.1,0),
sigma = matrix(c(2, -0.8, -0.8, 2), ncol=2),
burst = "Drift and cov(x,y) > 0")
z <- c(u, v, w, x)
plot(z, addpoints = FALSE, perani = FALSE)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.