# setProcess: Construct usual processes on manifolds In FieldSim: Random Fields (and Bridges) Simulations

## Description

The function `setProcess` constructs usual processes on a specific manifold.

## Usage

 `1` ```setProcess(name,parameter,values,manifold,covf) ```

## Arguments

 `name` the name of the process (see details); `parameter` the parameters of the process (see details); `values` the values of the simulated (or given) sample path of the process; `manifold` the manifold of which the process is defined; `covf` the autocovariance function of the process.

## Details

We list here the different usual process.

## Value

an object of class `process`.

## Author(s)

Alexandre Brouste (http://perso.univ-lemans.fr/~abrouste/) and Sophie Lambert-Lacroix (http://membres-timc.imag.fr/Sophie.Lambert/).

## References

A. Brouste, J. Istas and S. Lambert-Lacroix (2010) On simulation of manifold indexed fractional Gaussian fields. A. Brouste, J. Istas and S. Lambert-Lacroix (2014) Fractional Gaussian bridges with the package `FieldSim`.

`fieldsim`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50``` ```# Load FieldSim library library(FieldSim) # Fractional Brownian field on [0,1]^2 plane.fBm<-setProcess("fBm-plane",0.7) str(plane.fBm) # Multifractional Brownian field on [0,1]^2 funcH<-function(xi){0.3+xi[1]*0.6} plane.mBm<-setProcess("mBm-plane",funcH) str(plane.mBm) # Fractional Brownian sheet on [0,1]^2 #plane.fBs<-setProcess("fBs-plane",c(0.9,0.3)) #str(plane.fBs) # Anisotropic fractional Brownian field on [0,1]^2 #plane.afBf<-setProcess("afBf-plane",list(H=0.7,theta1=pi/6,theta2=pi/3)) #str(plane.afBf) # Bifractional fractional Brownian field on [0,1]^2 #plane.2pfBm<-setProcess("2pfBm-plane",list(H=0.7,K=0.5)) #str(plane.2pfBm) # Spherical fractional Brownian field #sphere.fBm<-setProcess("fBm-sphere",0.3) #str(sphere.fBm) # Fractional Brownian field on the hyperboloid #hyper.fBm<-setProcess("fBm-hyperboloid",0.7) #str(hyper.fBm) # Bridge associated to the Fractional Brownian field on [0,1]^2 #Gamma<-matrix(c(1,0,0,0,1,1,1,1,1,1/2,1/2,0.5),3,4) #bridge.plane.fBm<-setProcess("bridge-fBm-plane",list(Gamma=Gamma,par=0.9)) #str(bridge.plane.fBm) # User defined process (see Brouste et al. 2010) #sphere<-setManifold("sphere") #user.sphere<-setProcess(name="user",manifold=sphere) #parameter<-0.7 #acov<-function(xi,xj){exp(-#[email protected]@distance(xi,xj)^{2*[email protected]})} #[email protected]<-parameter #[email protected]<-acov #fieldsim(user.sphere) #plot(user.sphere) ```

FieldSim documentation built on May 29, 2017, 2:10 p.m.