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java.lang.Object Processes.StochasticProcess
Abstract class implementing some methods for a one dimensional * stochastic process and leaving process specific details abstract to be * overridden in concrete subclasses.
* * The only abstract method is timeStep(int)
. All other methods provide
* default implementations. If you want a concrete one dimensional
* stochastic process all you need to do is to subclass from StochasticProcess
* and to define this one method or to call the constructor and to define the
* method in the body of the constructor call.
Path computation: the basic procedure is to continue a path which * has already been realized until time t from this time t to the horizon * (branching at time t). * Here we are simulating future scenarios conditional on the state at time t. * This is what is needed for the computation of conditional expectations * conditioning on all information available at time t. The computation of * entire paths is then merely a continuation from time t=0.
* *Time is measured in discrete units (the time step dt). Integer time t * corresponds to continuous time t*dt. The case dt=1 is the special case of a * sequential stochastic process.
* * @author Michael J. Meyer
Constructor Summary  
StochasticProcess(int T,
double dt,
double X_0)
Constructor performing all initializations but leaving the abstract * method timeStep(int) undefined. 
Method Summary  
double 
get_dt()
Size of time step. 
double[] 
get_path()
Reference to array path containing the path of ( this )
* process X, path[t]=X(t*dt). 
int 
get_T()
Number of time steps to horizon. 
double 
get_X_0()
Initial value X(0). 
void 
newPath()
Computes a new path from time t=0. 
void 
newPathBranch(int t)
Continues a path existing on [0,t] from time t to * the horizon, that is, computes path[s], s=t+1,...,T from path[u], u<=t * (branching a path at time t). 
void 
pathSegment(int t,
int s)
Computes a new path segment from time t to time s through all * intermediate times t+1,...,s1. 
int 
pathSegment(int t,
StoppingTime tau)
Computes a new path segment from time t to the random time tau>=t * and returns the value of the time tau >= t when the path is stopped. 
int 
pathSegment(StoppingTime tau)
Computes a new path segment from time t=0 to the random time tau and * returns the value of the time tau when the path is stopped. 
RandomVariable 
sampledAt(StoppingTime tau)
Computes the random variable X_tau, that is, X sampled at the * stopping time tau, where X denotes the current stochastic process * ( this ). 
void 
simulationInit(int t)
Sets up a path simulation (t=0) or a simulation of * branches of an existing path (t>0, conditional expectations). 
abstract void 
timeStep(int t)
Evolves a path from discrete time [0,t] to time t+1, that is, * computes path[t+1] from path[u], u<=t. 
void 
timeStep(int t,
int s)
Computes path[s] from path[u], u<=t. 
Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Constructor Detail 
public StochasticProcess(int T, double dt, double X_0)
Constructor performing all initializations but leaving the abstract
* method timeStep(int)
undefined. Instantiate a StochasticProcess by
* defining this method in the body of the constructor call.
Method Detail 
public int get_T()
Number of time steps to horizon.
public double get_dt()
Size of time step.
public double get_X_0()
Initial value X(0).
public double[] get_path()
Reference to array path containing the path of (this
)
* process X, path[t]=X(t*dt).
public void simulationInit(int t)
Sets up a path simulation (t=0) or a simulation of * branches of an existing path (t>0, conditional expectations). * Default: empty, nothing to do.
* * @param current time.
public abstract void timeStep(int t)
Evolves a path from discrete time [0,t] to time t+1, that is, * computes path[t+1] from path[u], u<=t.
* * @param current time.
public void newPathBranch(int t)
Continues a path existing on [0,t] from time t to * the horizon, that is, computes path[s], s=t+1,...,T from path[u], u<=t * (branching a path at time t).
* * Default implementation: calls to timeStep. * This is not the most efficient method, override if fastest * path computation is a concern. * * @param t time of branching.
public void newPath()
Computes a new path from time t=0.
public void timeStep(int t, int s)
Computes path[s] from path[u], u<=t.
* *Sometimes this can be accomplished in a single step without stepping * through intermediate times t+1,...,s1. In this case path computations * can often be sped up by sampling the path only at the times s which are * needed.
* *Default implementation: individual time steps, no efficiency gain. * This is meant to be overridden where possible but a default is * provided for convenience.
* * @param t current time. * @param s future time.
public void pathSegment(int t, int s)
Computes a new path segment from time t to time s through all
* intermediate times t+1,...,s1. It is assumed that a path has been
* computed up to time t.
* Default implementation: calls to timeStep
.
public int pathSegment(int t, StoppingTime tau)
Computes a new path segment from time t to the random time tau>=t * and returns the value of the time tau >= t when the path is stopped. * Default implementation: calls to timeStep.
* * @param t current time * @param tau random future time
public int pathSegment(StoppingTime tau)
Computes a new path segment from time t=0 to the random time tau and * returns the value of the time tau when the path is stopped. * Default implementation: calls to timeStep.
* * @param tau random time when path is stopped.
public RandomVariable sampledAt(StoppingTime tau)
Computes the random variable X_tau, that is, X sampled at the
* stopping time tau, where X denotes the current stochastic process
* (this
).


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