Processes
Class StoppableMarkovChain

java.lang.Object
  Processes.StochasticProcess
      Processes.MarkovChain
          Processes.StoppableMarkovChain

public abstract class StoppableMarkovChain

extends MarkovChain

A Markov chain with reward(t,j) if the chain is stopped * at time t in state j. The optimal stopping time is a * member variable computed by the constructor at initialization.

* *

The methods a(t,i), b(t,i) provide information about the * possible movements of the chain: at time t the chain can move * from state i only to the states j=a(t,i), a(t,i)+1,...,b(t,i). * This information speeds path computation.

* *

To instantiate a StoppableMarkovChain the abstract methods * reward(t,i), a(t,i), b(t,i) * as well as the transition probabilities super.q(t,i,j) * have to be defined.

* * @author Michael J. Meyer

Constructor Summary

StoppableMarkovChain(int T, double j_0)
Constructor.

Method Summary

abstract int	a(int t, int i) Lower bound for states.
abstract int	b(int t, int i) Upper bound for states.
StoppingTime	get_optimalStoppingTime() The optimal stopping time with respect to the reward function * and transition probabilities.
abstract double	reward(int t, int i) Reward from stopping at time t if the chain is in state i.

Methods inherited from class Processes.MarkovChain

q, timeStep

Methods inherited from class Processes.StochasticProcess

get_dt, get_path, get_T, get_X_0, newPath, newPathBranch, pathSegment, pathSegment, pathSegment, sampledAt, simulationInit, timeStep

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

StoppableMarkovChain

public StoppableMarkovChain(int T,
                            double j_0)

Constructor. To instantiate a StoppableMarkovChain extend this class * and define the abstract methods reward(t,i), a(t,i), b(t,i) * as well as the transition probabilities super.q(t,i,j) or * call the constructor and define these methods in the body of the * constructor call.

* * @param T number of time steps to horizon * @param j_0 initial state

Method Detail

get_optimalStoppingTime

public StoppingTime get_optimalStoppingTime()

The optimal stopping time with respect to the reward function * and transition probabilities.

reward

public abstract double reward(int t,
                              int i)

Reward from stopping at time t if the chain is in state i.

* * @param t Current time. * @param i Current state.

a

public abstract int a(int t,
                      int i)

Lower bound for states. At time t only the states j=a(t,i),...,b(t,i) * can be reached from state i in the next step.

* * @param t Current time. * @param i Current state.

b

public abstract int b(int t,
                      int i)

Upper bound for states. At time t only the states j=a(t,i),...,b(t,i) * can be reached from state i in the next step.

* * @param t Current time. * @param i Current state.