simm.brown {adehabitatLT}  R Documentation 
This function simulates a Bivariate Brownian Motion.
simm.brown(date = 1:100, x0 = c(0, 0), h = 1, 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 
h 
Scaling parameter for the brownian motion (larger values give smaller dispersion) 
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 
A bivariate Brownian motion can be described by a vector
B2(t) = (Bx(t), By(t))
, where Bx
and By
are
unidimensional Brownian motions. Let F(t)
the set of all
possible realisations of the process (B2(s), 0 < s < t)
.
F(t)
therefore corresponds to the known information at time
t
. The properties of the bivariate Brownian motion are
therefore the following: (i) B2(0)= c(0,0)
(no uncertainty at
time t = 0
); (ii) B2(t)  B2(s)
is independent of
F(s)
(the next increment does not depend on the present or past
location); (iii) B2(t)  B2(s)
follows a bivariate normal
distribution with mean c(0,0)
and with variance equal to
(ts)
.
Note that for a given parameter h
, the process 1/h * B2(
t * h^2 )
is a Brownian motion. The function simm.brown
simulates the process B2(t * h^2)
. Note that the function
hbrown
allows the estimation of this scaling factor from data.
An object of class ltraj
Clement Calenge clement.calenge@ofb.gouv.fr
Stephane Dray dray@biomserv.univlyon1.fr
Manuela Royer royer@biomserv.univlyon1.fr
Daniel Chessel chessel@biomserv.univlyon1.fr
~put references to the literature/web site here ~
plot(simm.brown(1:1000), addpoints = FALSE) ## Note the difference in dispersion: plot(simm.brown(1:1000, h = 4), addpoints = FALSE)