BrownianGenerator

A Java module for the generation of multidimensional Brownian motions.

Theory

The theory behind this module can be found in the PDF report Decomposing_the_standard_Brownian_Motion_along_the_non_normalized_Faber_Schauder_System.pdf.

Usage

This Java Toolbox is packed in a .jar archive.

Package Usage

The source classes can be copied besides any other source code, and compiled alongside them. This enables one to call the methods directly in its program.

Command Line Usage

Java is needed in order to execute the .jar directly, the command line format being the following:

java -jar BrownianGenerator.jar kt=... [d=...] [c=...] [n=...] [start=...] [output=...]

Where option names are directly linked to the degrees of freedom detailed below:

• kt: number of discretisation points for the time interval (mandatory),
• d: dimension of the wanted Brownian motion (optionnal, default at 1),
• c: length of the wanted Brownian (optionnal, default at 1),
• N: cut parameter (see report, optionnal, default at 15),
• output: output file (optionnal, default is the standard output).

If an output file is specified for a default 1000-point 2-D Brownian motion will start like so:

kt=1000; d=2; c=1.0; n=15; startPoint=[0.0, 0.0]
0.0000000000000000e+00  0.0000000000000000e+00
3.8088021391987150e-02 -2.9328389173551024e-02
7.5191443043892860e-02 -5.5503525835590165e-02
9.3114861759012070e-02 -2.0253303573377730e-02

Examples of Command Line Calls :

java -jar BrownianGenerator.jar kt=10
java -jar BrownianGenerator.jar kt=10 d=2
java -jar BrownianGenerator.jar kt=10 c=14.5
java -jar BrownianGenerator.jar kt=10 n=5
java -jar BrownianGenerator.jar kt=10 start=[1]
java -jar BrownianGenerator.jar kt=10 d=2 start=[1,1]
java -jar BrownianGenerator.jar kt=10 start=[10.45]
java -jar BrownianGenerator.jar kt=10 d=3 start=[10.8,4.6,1.4e6]
java -jar BrownianGenerator.jar kt=10 d=2 output=test.txt
java -jar BrownianGenerator.jar kt=10 d=2 c=10 n=7 start=[0.0,1.47] output=brownian.txt