OrnsteinUhlenbeckProcess.java

/*
 * Class:        OrnsteinUhlenbeckProcess
 * 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.*;

public class OrnsteinUhlenbeckProcess extends StochasticProcess {
   protected NormalGen gen;
   protected double alpha, beta, sigma;
   // Precomputed values
   protected double[] badt, alphadt, sigmasqrdt;

   public OrnsteinUhlenbeckProcess(double x0, double alpha, double b, double sigma, RandomStream stream) {
      this(x0, alpha, b, sigma, new NormalGen(stream));
   }

   public OrnsteinUhlenbeckProcess(double x0, double alpha, double b, double sigma, NormalGen gen) {
      this.alpha = alpha;
      this.beta = b;
      this.sigma = sigma;
      this.x0 = x0;
      this.gen = gen;
   }
 
   public double nextObservation() {
      double xOld = path[observationIndex];
      double x = badt[observationIndex] + xOld * alphadt[observationIndex]
            + sigmasqrdt[observationIndex] * gen.nextDouble();
      observationIndex++;
      path[observationIndex] = x;
      return x;
   }

   public double nextObservation(double nextTime) {
      double previousTime = t[observationIndex];
      double xOld = path[observationIndex];
      observationIndex++;
      t[observationIndex] = nextTime;
      double dt = nextTime - previousTime;
      double tem = Math.exp(-alpha * dt);
      double tem1 = -Math.expm1(-alpha * dt);
      double x = tem * xOld + beta * tem1 + sigma * Math.sqrt(tem1 * (1.0 + tem) / (2.0 * alpha)) * gen.nextDouble();
      path[observationIndex] = x;
      return x;
   }

   public double nextObservation(double x, double dt) {
      double tem = Math.exp(-alpha * dt);
      double tem1 = -Math.expm1(-alpha * dt);
      x = tem * x + beta * tem1 + sigma * Math.sqrt(tem1 * (1.0 + tem) / (2.0 * alpha)) * gen.nextDouble();
      return x;
   }
 
   public double[] generatePath() {
      double x;
      double xOld = x0;
      for (int j = 0; j < d; j++) {
         x = badt[j] + xOld * alphadt[j] + sigmasqrdt[j] * gen.nextDouble();
         path[j + 1] = x;
         xOld = x;
      }
      observationIndex = d;
      return path;
   }

   public double[] generatePath(RandomStream stream) {
      gen.setStream(stream);
      return generatePath();
   }

   public void setParams(double x0, double alpha, double b, double sigma) {
      this.alpha = alpha;
      this.beta = b;
      this.sigma = sigma;
      this.x0 = x0;
      if (observationTimesSet)
         init(); // Otherwise not needed.
   }

   public void setStream(RandomStream stream) {
      gen.setStream(stream);
   }

   public RandomStream getStream() {
      return gen.getStream();
   }

   public double getAlpha() {
      return alpha;
   }

   public double getB() {
      return beta;
   }

   public double getSigma() {
      return sigma;
   }

   public NormalGen getGen() {
      return gen;
   }
 
   protected void initArrays(int d) {
      double dt, tem, tem1;
      for (int j = 0; j < d; j++) {
         dt = t[j + 1] - t[j];
         tem = Math.exp(-alpha * dt);
         tem1 = -Math.expm1(-alpha * dt);
         badt[j] = beta * tem1;
         alphadt[j] = tem;
         sigmasqrdt[j] = sigma * Math.sqrt(tem1 * (1.0 + tem) / (2.0 * alpha));
      }
   }
 
   // This is called by setObservationTimes to precompute constants
   // in order to speed up the path generation.
   protected void init() {
      super.init();
      badt = new double[d];
      alphadt = new double[d];
      sigmasqrdt = new double[d];
      initArrays(d);
   }
 
}