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();
    }
}