# simul.wiener: Wiener process simulation In far: Modelization for Functional AutoRegressive Processes

## Description

Simulation of Wiener processes.

## Usage

 `1` ```simul.wiener(m=64, n=1, m2=NULL) ```

## Arguments

 `m` Integer. Number of discretization points. `n` Integer. Number of observations. `m2` Integer. Length of the Karhunen-Loève expansion (2`m` by default).

## Details

This function use the known Karhunen-Loève expansion of Wiener processes to simulate observations of such a process.

The option `m2` is internally used to set the length of the expansion. This expansion need to be larger than the number of discretization points, but a too important value may slow down the generation. The default value as been chosen as a compromise.

## Value

A `fdata` object containing one variable ("var") which is a Wiener process of length `n` with `m` discretization points.

J. Damon

## References

Pumo, B. (1992). Estimation et Prévision de Processus Autoregressifs Fonctionnels. Applications aux Processus à Temps Continu. PhD Thesis, University Paris 6, Pierre et Marie Curie.

`simul.far.sde`, `simul.far.wiener`, `simul.farx`, `simul.far`.

## Examples

 ```1 2 3 4 5``` ``` noise <- simul.wiener(m=64,n=100,m2=512) summary(noise) par(mfrow=c(2,1)) plot(noise,date=1) plot(select.fdata(noise,date=1:5),whole=TRUE,separator=TRUE) ```

### Example output

```Loading required package: nlme
far library : Modelization for Functional AutoRegressive processes

version 0.6-4 (2014-12-07)

Variable:  var
Mean of the norms:
L1 norm   L2 norm Linf norm
0.5243715 0.6099706 1.1571603
```

far documentation built on May 2, 2019, 9:28 a.m.