NormalInverseGaussianProcess.java

/*
 * Class:        NormalInverseGaussianProcess
 * Description:  
 * Environment:  Java
 * Software:     SSJ 
 * Copyright (C) 2001  Pierre L'Ecuyer and Universite de Montreal
 * Organization: DIRO, Universite de Montreal
 * @author       
 * @since
 *
 *
 * 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.
 *
 */
package umontreal.ssj.stochprocess;
 
import umontreal.ssj.rng.*;
import umontreal.ssj.probdist.*;
import umontreal.ssj.randvar.*;
import umontreal.ssj.hups.*;

public class NormalInverseGaussianProcess extends StochasticProcess {
   protected RandomStream streamIG1; // U[0,1) gen used in the inverse gaussian
   protected RandomStream streamIG2; // U[0,1) gen used (maybe) in the inverse gaussian
   protected RandomStream streamBrownian; // U[0,1) gen for the normal "Brownian"
 
   protected InverseGaussianProcess igProcess;
   protected NormalGen normalGen;
   // Randomized time generated by the InverseGaussianProcess.
   protected double[] stochTime;
   double[] dt;
   double[] mudt;
 
   // Parameters of the normal inverse gaussian
   protected double mu;
   protected double delta;
   protected double alpha;
   protected double beta;
   protected double gamma;

   public NormalInverseGaussianProcess(double x0, double alpha, double beta, double mu, double delta,
         RandomStream streamBrownian, InverseGaussianProcess igP) {
      setParams(x0, alpha, beta, mu, delta);
      this.streamBrownian = streamBrownian;
      normalGen = new NormalGen(streamBrownian); // N(0,1)
      igProcess = igP; // its params will be set in init().
      this.streamIG1 = igProcess.getStream();
      this.streamIG2 = streamIG1;
   }

   public NormalInverseGaussianProcess(double x0, double alpha, double beta, double mu, double delta,
         RandomStream streamBrownian, RandomStream streamIG1, RandomStream streamIG2, String igType) {
      setParams(x0, alpha, beta, mu, delta);
      this.streamIG1 = streamIG1;
      this.streamIG2 = streamIG2;
      this.streamBrownian = streamBrownian;
      normalGen = new NormalGen(streamBrownian); // N(0,1)
 
      // The initial time of igProcess here, 0., is arbitrary:
      // init() sets igProcess.x0 = t[0].
      if (igType.compareTo("SEQUENTIAL_SLOW") == 0)
         // the initial value, 0.0, of the IG will be overriden by
         // the initial time, when it will be set.
         igProcess = new InverseGaussianProcess(0.0, delta, gamma, streamIG1);
      else if (igType.compareTo("SEQUENTIAL_MSH") == 0)
         igProcess = new InverseGaussianProcessMSH(0.0, delta, gamma, streamIG1, streamIG2);
      else if (igType.compareTo("BRIDGE") == 0)
         igProcess = new InverseGaussianProcessBridge(0.0, delta, gamma, streamIG1, streamIG2);
      else if (igType.compareTo("PCA") == 0)
         igProcess = new InverseGaussianProcessPCA(0.0, delta, gamma, streamIG1);
      else
         throw new IllegalArgumentException("Unrecognized igType");
   }

   public NormalInverseGaussianProcess(double x0, double alpha, double beta, double mu, double delta,
         RandomStream streamAll, String igType) {
      this(x0, alpha, beta, mu, delta, streamAll, streamAll, streamAll, igType);
   }

   public double[] generatePath() {
      if (igProcess.getNumberOfRandomStreams() != 1)
         return generatePathTwoIGStreams();
 
      double x = x0;
      double[] randomNormal = new double[d];
      double[] randomIG1 = new double[d];
      for (int j = 0; j < d; j++) {
         randomIG1[j] = streamIG1.nextDouble();
         randomNormal[j] = streamBrownian.nextDouble();
      }
 
      stochTime = igProcess.generatePath(randomIG1);
      for (int j = 0; j < d; j++) {
         double dy = stochTime[j + 1] - stochTime[j];
         x += mudt[j] + beta * dy + Math.sqrt(dy) * NormalDistQuick.inverseF01(randomNormal[j]);
         path[j + 1] = x;
      }
      observationIndex = d;
      return path;
   }
 
   protected double[] generatePathTwoIGStreams() {
      double x = x0;
      double[] uniformNormal = new double[d];
      double[] uniformIG1 = new double[d];
      double[] uniformIG2 = new double[d];
 
      for (int j = 0; j < d; j++) {
         uniformIG1[j] = streamIG1.nextDouble();
         uniformNormal[j] = streamBrownian.nextDouble();
         uniformIG2[j] = streamIG2.nextDouble();
      }
 
      stochTime = igProcess.generatePath(uniformIG1, uniformIG2);
      for (int j = 0; j < d; j++) {
         double dy = stochTime[j + 1] - stochTime[j];
         x += mudt[j] + beta * dy + Math.sqrt(dy) * NormalDistQuick.inverseF01(uniformNormal[j]);
         path[j + 1] = x;
      }
      observationIndex = d;
      return path;
   }

   public double nextObservation() {
      double igNext = igProcess.nextObservation();
      observationIndex = igProcess.getCurrentObservationIndex();
      stochTime[observationIndex] = igNext;
      double dY = igNext - stochTime[0];
      double dT = t[observationIndex] - t[0];
      path[observationIndex] = x0 + mu * dT + beta * dY + Math.sqrt(dY) * normalGen.nextDouble();
      return path[observationIndex];
   }
 
   protected void init() {
      super.init();
      igProcess.setParams(delta, gamma);
      if (observationTimesSet) {
         stochTime = new double[d + 1];
         stochTime[0] = t[0];
         dt = new double[d];
         mudt = new double[d];
         for (int i = 0; i < d; i++) {
            dt[i] = t[i + 1] - t[i];
            mudt[i] = dt[i] * mu;
         }
      }
   }

   public void setObservationTimes(double t[], int d) {
      super.setObservationTimes(t, d);
      igProcess.setObservationTimes(t, d);
      igProcess.x0 = t[0];
   }

   public void setParams(double x0, double alpha, double beta, double mu, double delta) {
      // Initializes the parameters of the process
      if (delta <= 0.0)
         throw new IllegalArgumentException("delta <= 0");
      if (alpha <= 0.0)
         throw new IllegalArgumentException("alpha <= 0");
      if (Math.abs(beta) >= alpha)
         throw new IllegalArgumentException("|beta| >= alpha");
 
      this.x0 = x0;
      this.mu = mu;
      this.delta = delta;
      this.beta = beta;
      this.alpha = alpha;
 
      gamma = Math.sqrt(alpha * alpha - beta * beta);
      if (observationTimesSet)
         init();
   }

   public double getAlpha() {
      return alpha;
   }

   public double getBeta() {
      return beta;
   }

   public double getMu() {
      return mu;
   }

   public double getDelta() {
      return delta;
   }

   public double getGamma() {
      return gamma;
   }

   public double getAnalyticAverage(double time) {
      return mu * time + delta * time * beta / gamma;
   }

   public double getAnalyticVariance(double time) {
      return delta * time * alpha * alpha / gamma / gamma / gamma;
   }

   public RandomStream getStream() {
      if ((streamIG1 != streamIG2) || (streamIG1 != streamBrownian) || (streamIG1 != normalGen.getStream())
            || (streamIG1 != igProcess.getStream()))
         throw new UnsupportedOperationException("Two different streams or more are present");
      return streamIG1;
   }

   public void setStream(RandomStream stream) {
      streamIG1 = streamIG2 = streamBrownian = stream;
      normalGen.setStream(stream);
      igProcess.setStream(stream);
   }
 
}