BrownianTemporalPDF.java
package org.drip.sample.kolmogorov;
import org.drip.dynamics.ito.TimeR1Vertex;
import org.drip.dynamics.kolmogorov.R1FokkerPlanckBrownian;
import org.drip.dynamics.process.R1ProbabilityDensityFunction;
import org.drip.numerical.common.FormatUtil;
import org.drip.service.env.EnvManager;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting risk, transaction costs, exposure, margin
* calculations, valuation adjustment, and portfolio construction within and across fixed income,
* credit, commodity, equity, FX, and structured products.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
*
* DROP Analytics Core implements libraries for the following:
* - Fixed Income Analytics
* - Asset Backed Analytics
* - XVA Analytics
* - Exposure and Margin Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Transaction Cost Analytics
*
* DROP Numerical Core implements libraries for the following:
* - Statistical Learning Library
* - Numerical Optimizer Library
* - Machine Learning Library
* - Spline Builder Library
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>BrownianTemporalPDF</i> illustrates the Temporal Distribution of an Evolving R<sup>1</sup> Brownian
* Motion. The References are:
*
* <br><br>
* <ul>
* <li>
* Bogoliubov, N. N., and D. P. Sankevich (1994): N. N. Bogoliubov and Statistical Mechanics
* <i>Russian Mathematical Surveys</i> <b>49 (5)</b> 19-49
* </li>
* <li>
* Holubec, V., K. Kroy, and S. Steffenoni (2019): Physically Consistent Numerical Solver for
* Time-dependent Fokker-Planck Equations <i>Physical Review E</i> <b>99 (4)</b> 032117
* </li>
* <li>
* Kadanoff, L. P. (2000): <i>Statistical Physics: Statics, Dynamics, and Re-normalization</i>
* <b>World Scientific</b>
* </li>
* <li>
* Ottinger, H. C. (1996): <i>Stochastic Processes in Polymeric Fluids</i> <b>Springer-Verlag</b>
* Berlin-Heidelberg
* </li>
* <li>
* Wikipedia (2019): Fokker-Planck Equation
* https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/AnalyticsCore.md">Analytics Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/FixedIncomeAnalyticsLibrary.md">Fixed Income Analytics</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/README.md">Dynamics</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/dynamics/lmm/README.md">LIBOR Market Model</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class BrownianTemporalPDF
{
public static final void main (
final String[] argumentArray)
throws Exception
{
EnvManager.InitEnv (
""
);
double[] timeArray =
{
0.5,
1.0,
1.5,
2.0,
2.5,
3.0,
3.5,
4.0,
4.5,
5.0,
5.5,
6.0,
6.5,
7.0,
7.5,
8.0,
8.5,
9.0,
9.5
};
double[] xArray =
{
-2.5,
-2.0,
-1.5,
-1.0,
-0.5,
0.0,
0.5,
1.0,
1.5,
2.0,
2.5,
};
R1ProbabilityDensityFunction r1ProbabilityDensityFunction =
new R1FokkerPlanckBrownian().deltaStartTemporalPDF (
0.
);
System.out.println ("\t|-------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| FOKKER PLANCK BROWNIAN MOTION DISTRIBUTION REALIZATIONS OVER TIME ||");
System.out.println ("\t|-------------------------------------------------------------------------------------------------------------------------------------------||");
System.out.println ("\t| L -> R: ||");
System.out.println ("\t| - Time ||");
System.out.println ("\t| - Row of PDF Values over x ||");
System.out.println ("\t|-------------------------------------------------------------------------------------------------------------------------------------------||");
for (double t : timeArray)
{
java.lang.String dump = "\t| " + FormatUtil.FormatDouble (t, 1, 1, 1.) + " =>";
for (double x : xArray)
{
dump = dump + " " + FormatUtil.FormatDouble (
r1ProbabilityDensityFunction.density (
new TimeR1Vertex (
t,
x
)
), 1, 6, 1.
) + " |";
}
System.out.println (dump + "|");
}
System.out.println ("\t|-------------------------------------------------------------------------------------------------------------------------------------------||");
EnvManager.TerminateEnv();
}
}