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\name{RMlsfbm}
\alias{RMlsfbm}
\title{Locally Positive Definite Function Given by the Fractal Brownian Motion}
\description{
\command{\link{RMlsfbm}} is a positive definite function on the
unit ball in \eqn{R^d} centred at the origin,
\deqn{C(r) = c - r^\alpha}{C(r) = c - r^\alpha}
with \eqn{r = \|x- y\|\in [0,1]}{0 <= r = || x - y || <= 1}.
}
\usage{
RMlsfbm(alpha, const, var, scale, Aniso, proj)
}
\arguments{
\item{alpha}{numeric in \eqn{(0,2)}; refers to the fractal dimension of the
process.}
\item{const}{the \code{const}ant \eqn{c} is given by the
formula
\deqn{
c = 2^{-\alpha} \Gamma(d / 2 + \alpha/2) \Gamma(1 - \alpha/2) /
\Gamma(d / 2)
}
and should not be changed by the user in order to ensure positive
definiteness.
}
\item{var,scale,Aniso,proj}{optional arguments; same meaning for any
\command{\link{RMmodel}}. If not passed, the above
covariance function remains unmodified.}
}
\value{
\command{\link{RMlsfbm}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}.
}
\references{
\itemize{
\item Martini, J., Schlather, M., Simianer, H. (In preparation.)
}
}
\me
\seealso{
\command{\link{RMbcw}} generalizes \command{RMlsfbm} in case that \eqn{c}
is given,
\command{\link{RMfbm}},
\command{\link{RMmodel}},
\command{\link{RFsimulate}},
\command{\link{RFfit}}.
}
\keyword{spatial}
\keyword{models}
\examples{\dontshow{StartExample()}
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
model <- RMlsfbm(alpha=1, scale=10)
x <- seq(0, 10, 0.02)
plot(model, xlim=c(0,10))
plot(RFsimulate(model, x=x))
\dontshow{FinalizeExample()}}
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