Class IndependentIncrementsFromICDF

  • All Implemented Interfaces:
    Serializable, IndependentIncrements

    public class IndependentIncrementsFromICDF
    extends Object
    implements IndependentIncrements, Serializable
    Implementation of a time-discrete n-dimensional sequence of independent increments W = (W1,...,Wn) form a given set of inverse cumulative distribution functions. Independent increments is a sequence of independent random variables index by the time index associated with the time discretization. At each time step the increment is a d-dimensional random variable \( Z(t_{i}) \), where d is numberOfFactors. where each component of \( Z_{j}(t_{i}) \) is given by \[ Z_{j}(t_{i}) = ICDF_{i,j}(U_{i,j}) \] for a sequence of independent uniform distributes random variables U_{i,j}. The inverse cumulative distribution functions \( ICDF_{i,j} \) are given by inverseCumulativeDistributionFunctions as the map \( i \mapsto ( j \mapsto ICDF_{i,j} ) \) (here i is the time index and j is the factor (component). Each \( U_{i,j} \) is samples using numberOfPaths. The class is immutable and thread safe. It uses lazy initialization.
    Version:
    1.6
    Author:
    Christian Fries
    See Also:
    Serialized Form
    • Constructor Detail

      • IndependentIncrementsFromICDF

        public IndependentIncrementsFromICDF​(TimeDiscretization timeDiscretization,
                                             int numberOfFactors,
                                             int numberOfPaths,
                                             int seed,
                                             IntFunction<IntFunction<DoubleUnaryOperator>> inverseCumulativeDistributionFunctions,
                                             RandomVariableFactory randomVariableFactory)
        Construct the simulation of independent increments. Independent increments is a sequence of independent random variables index by the time index associated with the time discretization. At each time step the increment is a d-dimensional random variable \( Z(t_{i}) \), where d is numberOfFactors. where each component of \( Z_{j}(t_{i}) \) is given by \[ Z_{j}(t_{i}) = ICDF_{i,j}(U_{i,j}) \] for a sequence of independent uniform distributes random variables U_{i,j}. The inverse cumulative distribution functions \( ICDF_{i,j} \) are given by inverseCumulativeDistributionFunctions as the map \( i \mapsto ( j \mapsto ICDF_{i,j} ) \) (here i is the time index and j is the factor (component). Each \( U_{i,j} \) is samples using numberOfPaths. The constructor allows to set the factory to be used for the construction of random variables. This allows to generate increments represented by different implementations of the RandomVariable (e.g. the RandomVariableFromFloatArray internally using float representations).
        Parameters:
        timeDiscretization - The time discretization used for the increments.
        numberOfFactors - Number of factors.
        numberOfPaths - Number of paths to simulate.
        seed - The seed of the random number generator.
        inverseCumulativeDistributionFunctions - A map from the timeIndices to a map from the from the factors to the corresponding inverse cumulative distribution function.
        randomVariableFactory - Factory to be used to create random variable.
      • IndependentIncrementsFromICDF

        public IndependentIncrementsFromICDF​(TimeDiscretization timeDiscretization,
                                             int numberOfFactors,
                                             int numberOfPaths,
                                             int seed,
                                             IntFunction<IntFunction<DoubleUnaryOperator>> inverseCumulativeDistributionFunctions)
        Construct the simulation of independet increments. The independent increments is a sequence of independent random variables index by the time index associated with the time discretization. At each time step the increment is a d-dimensional random variable \( Z(t_{i}) \), where d is numberOfFactors. where each component of \( Z_{j}(t_{i}) \) is given by \[ Z_{j}(t_{i}) = ICDF_{i,j}(U_{i,j}) \] for a sequence of independent uniform distributes random variables U_{i,j}. The inverse cumulative distribution functions \( ICDF_{i,j} \) are given by inverseCumulativeDistributionFunctions as the map \( i \mapsto ( j \mapsto ICDF_{i,j} ) \) (here i is the time index and j is the factor (component). Each \( U_{i,j} \) is samples using numberOfPaths.
        Parameters:
        timeDiscretization - The time discretization used for the increments.
        numberOfFactors - Number of factors.
        numberOfPaths - Number of paths to simulate.
        seed - The seed of the random number generator.
        inverseCumulativeDistributionFunctions - A map from the timeIndices to a map from the from the factors to the corresponding inverse cumulative distribution function.
    • Method Detail

      • getCloneWithModifiedSeed

        public IndependentIncrements getCloneWithModifiedSeed​(int seed)
        Description copied from interface: IndependentIncrements
        Return a new object implementing BrownianMotion having the same specifications as this object but a different seed for the random number generator. This method is useful if you like to make Monte-Carlo samplings by changing the seed.
        Specified by:
        getCloneWithModifiedSeed in interface IndependentIncrements
        Parameters:
        seed - New value for the seed.
        Returns:
        New object implementing BrownianMotion.
      • getIncrement

        public RandomVariable getIncrement​(int timeIndex,
                                           int factor)
        Description copied from interface: IndependentIncrements
        Return the increment for a given timeIndex and given factor. The method returns the random variable Δ Xj(ti) := Xj(ti+1)-X(ti) for the given time index i and a given factor (index) j
        Specified by:
        getIncrement in interface IndependentIncrements
        Parameters:
        timeIndex - The time index (corresponding to the this class's time discretization)
        factor - The index of the factor (independent scalar increment)
        Returns:
        The factor (component) of the increments (a random variable)
      • getRandomVariableForConstant

        public RandomVariable getRandomVariableForConstant​(double value)
        Description copied from interface: IndependentIncrements
        Returns a random variable which is initialized to a constant, but has exactly the same number of paths or discretization points as the ones used by this BrownianMotion.
        Specified by:
        getRandomVariableForConstant in interface IndependentIncrements
        Parameters:
        value - The constant value to be used for initialized the random variable.
        Returns:
        A new random variable.
      • getSeed

        public int getSeed()
        Returns:
        Returns the seed.
      • hashCode

        public int hashCode()
        Overrides:
        hashCode in class Object