Simulation methods for BrownResnick processes
Description
These models define the particular way to simulate BrownResnick processes
Usage
1 2 3 4 5 6  RPbrmixed(phi, tcf, xi, mu, s, meshsize, vertnumber, optim_mixed,
optim_mixed_tol, optim_mixed_maxpo, lambda, areamat, variobound)
RPbrorig(phi, tcf, xi, mu, s)
RPbrshifted(phi, tcf, xi, mu, s)

Arguments
phi 
object of class 
tcf 
the extremal correlation function; either 
xi, mu, s 
the shape parameter, the location parameter and the scale parameter, respectively, of the generalized extreme value distribution. See Details. 
lambda 
positive constant factor in the intensity of the Poisson
point processused in the M3 representation, cf. Thm. 6 and Remark 7
in Oesting et. al (2012); can be estimated by setting

areamat 
vector or matrix of values in [0,1] with odd
length (odd number of rows and columns, respectively). Each value
represents the portion of processes whose maximum is located at a
specific location on a grid taken into account for the simulation
of the shape function in the M3 representation. The center of

meshsize, vertnumber, optim_mixed,
optim_mixed_tol, optim_mixed_maxpo, variobound 
further arguments
for simulation via the mixed moving maxima (M3) representation; see

Details
The argument xi
is always a number, i.e. ξ is constant
in space. In contrast, μ and s might be constant
numerical value or given a RMmodel
, in particular by a
RMtrend
model.
The functions RPbrorig
, RPbrshifted
and RPbrmixed
simulate a BrownResnick process, which is defined by
Z(x) = max_{i=1, 2, ...} X_i * exp(W_i(x)  gamma),
where the X_i are the points of a Poisson point process on the
positive real halfaxis with intensity 1/x^2 dx,
W_i ~ Y are iid centered Gaussian processes with
stationary increments and variogram gamma given by
model
. The functions correspond to the following ways of
simulation:
RPbrorig
simulation via using the original definition (method 0 in Oesting et al., 2012)
RPbrshifted
simulation using a random shift (similar to method 1 and 2)
RPbrmixed
simulation using M3 representation (method 4)
Value
The functions return an object of class
RMmodel
Note
Advanced options for RPbroriginal
and RPbrshifted
are maxpoints
and max_gauss
, see RFoptions
.
Author(s)
Marco Oesting, oesting@math.unimannheim.de, Martin Schlather, schlather@math.unimannheim.de http://ms.math.unimannheim.de/de/publications/software
References
Oesting, M., Kabluchko, Z. and Schlather M. (2012) Simulation of BrownResnick Processes, Extremes, 15, 89107.
See Also
RPbrownresnick
,
RMmodel
,
RPgauss
,
maxstable
,
maxstableAdvanced
Examples
1 2 3 4 5 6  RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
## currently does not work

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