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java.lang.Objectch.epfl.lis.sde.solver.SdeSolver
ch.epfl.lis.sde.solver.MilsteinIto
public class MilsteinIto
This class implements the explicit Milstein method (strong order of convergence 1) to be used with SDEs using Ito scheme. The iterative Milstein scheme is given by the formula [1] Xn+1 = Xn + Fn*h + Gn*dWn + 0.5*Gn*Gn'*(dWn^2 - h) (Ito) <-- Implemented here! Xn+1 = Xn + Fn*h + Gn*dWn + 0.5*Gn*Gn'*(dWn^2) (Stratonovich) where h is the integration step size. This solver implements a first-order stochastic Runge-Kutta algorithm (FSRK) that does not need the user to specify explicitly the derivative of the diffusion term G'. [1] [1] P.E. Kloeden, E. Platen, and H. Schurz, Numerical solution of SDE through computer experiments, Springer, 1994. (pp 150-153) [2] http://en.wikipedia.org/wiki/Runge-Kutta_method_(SDE)
Constructor Summary | |
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MilsteinIto()
Default constructor |
Method Summary | |
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void |
advance(double t,
double h,
cern.colt.matrix.DoubleMatrix1D dW,
cern.colt.matrix.DoubleMatrix1D dZ,
cern.colt.matrix.DoubleMatrix1D Xin,
cern.colt.matrix.DoubleMatrix1D Xout)
Proceed on iteration of the numerical integration (step size = h) |
java.lang.String |
getDescription()
Returns a description for this solver. |
void |
init()
Initialization of the solver. |
void |
reset()
Cleanup the solver |
Methods inherited from class ch.epfl.lis.sde.solver.SdeSolver |
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checkConvergence, checkX, converged, generateW, generateWienerIncrements, generateWZ, getAbsolutePrecision, getH, getRelativePrecision, getSystem, getX, integrate, setAbsolutePrecision, setH, setRelativePrecision, setSystem, setX, step |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public MilsteinIto()
Method Detail |
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public void reset()
reset
in class SdeSolver
public void init() throws java.lang.IllegalArgumentException
init
in class SdeSolver
java.lang.IllegalArgumentException
public void advance(double t, double h, cern.colt.matrix.DoubleMatrix1D dW, cern.colt.matrix.DoubleMatrix1D dZ, cern.colt.matrix.DoubleMatrix1D Xin, cern.colt.matrix.DoubleMatrix1D Xout) throws java.lang.Exception
advance
in class SdeSolver
java.lang.Exception
public java.lang.String getDescription()
getDescription
in class SdeSolver
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