Class MultivariateBrownianRRG

  • All Implemented Interfaces:
    Seedable, MultivariateRandomRealizationGenerator

    public class MultivariateBrownianRRG
    extends Object
    implements MultivariateRandomRealizationGenerator
    This is the Random Walk construction of a multivariate Brownian motion.

    For constant μ and σ, this method is exact in the sense that the joint distribution of the simulated values coincides with the joint distribution of the corresponding Brownian motion a the time grid points. Please note that this says nothing about what happens between two successive grid points.

    For time-dependent μ and σ, this method in general introduce discretization error even at the time grid points, because the increments will no longer have exactly the correct mean and variance.

    • Constructor Detail

      • MultivariateBrownianRRG

        public MultivariateBrownianRRG​(int d,
                                       TimeGrid timePoints,
                                       Vector initial)
        Construct a random realization generator to produce multi-dimensional Brownian paths at time points specified.
        Parameters:
        d - the dimension of the Brownian motion
        timePoints - specifying the time points in a grid
        initial - the initial value of the process
      • MultivariateBrownianRRG

        public MultivariateBrownianRRG​(int d,
                                       TimeGrid timePoints)
        Construct a random realization generator to produce multi-dimensional Brownian paths at time points specified.
        Parameters:
        d - the dimension of the Brownian motion
        timePoints - specifying the time points in a grid
      • MultivariateBrownianRRG

        public MultivariateBrownianRRG​(int d,
                                       int T)
        Construct a random realization generator to produce multi-dimensional Brownian paths at evenly spaced time points [0, 1, ...].
        Parameters:
        d - the dimension of the Brownian motion
        T - the number of time points