net.finmath.montecarlo.process

Class LinearInterpolatedTimeDiscreteProcess

java.lang.Object

net.finmath.montecarlo.process.LinearInterpolatedTimeDiscreteProcess

All Implemented Interfaces:

Process

public class LinearInterpolatedTimeDiscreteProcess
extends Object
implements Process

A linear interpolated time discrete process, that is, given a collection of tuples (Double, RandomVariableFromDoubleArray) representing realizations \( X(t_{i}) \) this class implements the Process and creates a stochastic process \( t \mapsto X(t) \) where \[ X(t) = \frac{t_{i+1} - t}{t_{i+1}-t_{i}} X(t_{i}) + \frac{t - t_{i}}{t_{i+1}-t_{i}} X(t_{i+1}) \] with \( t_{i} \leq t \leq t_{i+1} \). Note: this is the interpolation scheme used in the convergence of the Euler-Maruyama scheme.

Version:

1.0

Author:

Christian Fries

Constructor Summary

Constructors

Constructor and Description
LinearInterpolatedTimeDiscreteProcess(Map<Double,RandomVariable> realizations) Create a time discrete process by linear interpolation of random variables.

Method Summary

Modifier and Type	Method and Description
LinearInterpolatedTimeDiscreteProcess	add(LinearInterpolatedTimeDiscreteProcess process) Create a new linear interpolated time discrete process by using the time discretization of this process and the sum of this process and the given one as its values.
LinearInterpolatedTimeDiscreteProcess	apply(DoubleUnaryOperator function) Create a new process consisting of the interpolation of the random variables obtained by applying the given function to this process discrete set of random variables.
Process	clone() Create and return a clone of this process.
RandomVariable	getMonteCarloWeights(int timeIndex) This method returns the weights of a weighted Monte Carlo method (the probability density).
int	getNumberOfComponents()
RandomVariable	getProcessValue(double time, int component) Returns the (possibly interpolated) value of this stochastic process at a given time \( t \).
RandomVariable	getProcessValue(int timeIndex, int component) This method returns the realization of a component of the process for a given time index.
double	getTime(int timeIndex)
TimeDiscretization	getTimeDiscretization()
int	getTimeIndex(double time) Returns the time index for a given simulation time.

Methods inherited from class java.lang.Object

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

Constructor Detail

LinearInterpolatedTimeDiscreteProcess

public LinearInterpolatedTimeDiscreteProcess(Map<Double,RandomVariable> realizations)

Create a time discrete process by linear interpolation of random variables.

Parameters:

realizations - Given map from time to random variable. The map must not be modified.

Method Detail

add

public LinearInterpolatedTimeDiscreteProcess add(LinearInterpolatedTimeDiscreteProcess process)
                                          throws CalculationException

Create a new linear interpolated time discrete process by using the time discretization of this process and the sum of this process and the given one as its values.

Parameters:

process - A given process.

Returns:

A new process representing the of this and the given process.

Throws:

CalculationException - Thrown if the given process fails to evaluate at a certain time point.

apply

public LinearInterpolatedTimeDiscreteProcess apply(DoubleUnaryOperator function)

Create a new process consisting of the interpolation of the random variables obtained by applying the given function to this process discrete set of random variables. That is \( t \mapsto Y(t) \) where \[ Y(t) = \frac{t_{i+1} - t}{t_{i+1}-t_{i}} f(X(t_{i})) + \frac{t - t_{i}}{t_{i+1}-t_{i}} f(X(t_{i+1})) \] with \( t_{i} \leq t \leq t_{i+1} \) and a given function \( f \).

Parameters:

function - The function \( f \), a univariate function.

Returns:

A new process consisting of the interpolation of the random variables obtained by applying the given function to this process discrete set of random variables.

getProcessValue

public RandomVariable getProcessValue(double time,
                                      int component)

Returns the (possibly interpolated) value of this stochastic process at a given time \( t \).

Parameters:

time - The time \( t \).

component - The component to be returned (if this is a vector valued process), otherwise 0.

Returns:

The random variable \( X(t) \).

getProcessValue

public RandomVariable getProcessValue(int timeIndex,
                                      int component)

Description copied from interface: Process

This method returns the realization of a component of the process for a given time index.

Specified by:

getProcessValue in interface Process

Parameters:

timeIndex - Time index at which the process should be observed

component - Component index of the process

Returns:

The process component realizations (given as RandomVariableFromDoubleArray)

getMonteCarloWeights

public RandomVariable getMonteCarloWeights(int timeIndex)

Description copied from interface: Process

This method returns the weights of a weighted Monte Carlo method (the probability density).

Specified by:

getMonteCarloWeights in interface Process

Parameters:

timeIndex - Time index at which the process should be observed

Returns:

A vector of positive weights which sums up to one

getNumberOfComponents

public int getNumberOfComponents()

Specified by:

getNumberOfComponents in interface Process

Returns:

Returns the numberOfComponents.

getTimeDiscretization

public TimeDiscretization getTimeDiscretization()

Specified by:

getTimeDiscretization in interface Process

Returns:

Returns the timeDiscretizationFromArray.

getTime

public double getTime(int timeIndex)

Specified by:

getTime in interface Process

Parameters:

timeIndex - Time index.

Returns:

Returns the time for a given time index.

getTimeIndex

public int getTimeIndex(double time)

Description copied from interface: Process

Returns the time index for a given simulation time.

Specified by:

getTimeIndex in interface Process

Parameters:

time - The given simulation time.

Returns:

Returns the time index for a given time

clone

public Process clone()

Description copied from interface: Process

Create and return a clone of this process. The clone is not tied to any model, but has the same process specification, that is, if the model is the same, it would generate the same paths.

Specified by:

clone in interface Process

Overrides:

clone in class Object

Returns:

Clone of the process