Package org.drip.dynamics.kolmogorov

Class RdFokkerPlanck

java.lang.Object

org.drip.dynamics.kolmogorov.RdFokkerPlanck

public class RdFokkerPlanck
extends java.lang.Object

RdFokkerPlanck exposes the R^d Fokker-Planck Probability Density Function Evolution Equation. The References are:

• Bogoliubov, N. N., and D. P. Sankevich (1994): N. N. Bogoliubov and Statistical Mechanics Russian Mathematical Surveys 49 (5) 19-49
• Holubec, V., K. Kroy, and S. Steffenoni (2019): Physically Consistent Numerical Solver for Time-dependent Fokker-Planck Equations Physical Review E 99 (4) 032117
• Kadanoff, L. P. (2000): Statistical Physics: Statics, Dynamics, and Re-normalization World Scientific
• Ottinger, H. C. (1996): Stochastic Processes in Polymeric Fluids Springer-Verlag Berlin-Heidelberg
• Wikipedia (2019): Fokker-Planck Equation https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation

• Module = Product Core Module
• Library = Fixed Income Analytics
• Project = HJM, Hull White, LMM, and SABR Dynamic Evolution Models
• Package = Fokker Planck Kolmogorov Forward/Backward

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
RdFokkerPlanck(RdToR1Drift[] driftFunctionArray, DiffusionTensor diffusionTensor, RiskenOmegaEstimator riskenOmegaEstimator)	RdFokkerPlanck Constructor

Method Summary

Modifier and Type	Method	Description
DiffusionTensor	diffusionTensor()	Retrieve the Diffusion Tensor
RdToR1Drift[]	driftFunctionArray()	Retrieve the Drift Function Array
double	pdfDot(RdProbabilityDensityFunction probabilityDensityFunction, TimeRdVertex timeRdVertex)	Compute the Next Incremental Time Derivative of the PDF
RiskenOmegaEstimator	riskenOmegaEstimator()	Retrieve the Risken Omega Estimator
RdToR1	steadyStatePDF()	Compute the Steady-State Probability Distribution Function, if any
RdProbabilityDensityFunction	temporalPDF(RdToR1 intialProbabilityDensityFunction)	Compute the Temporal Probability Distribution Function, if any

Methods inherited from class java.lang.Object

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

Constructor Details

RdFokkerPlanck

public RdFokkerPlanck(RdToR1Drift[] driftFunctionArray,
DiffusionTensor diffusionTensor,
RiskenOmegaEstimator riskenOmegaEstimator)
               throws java.lang.Exception

RdFokkerPlanck Constructor

Parameters:

driftFunctionArray - Drift Function Array

diffusionTensor - Diffusion Tensor

riskenOmegaEstimator - Risken Omega Estimator

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

driftFunctionArray

public RdToR1Drift[] driftFunctionArray()

Retrieve the Drift Function Array

Returns:

The Drift Function Array

diffusionTensor

public DiffusionTensor diffusionTensor()

Retrieve the Diffusion Tensor

Returns:

The Diffusion Tensor

riskenOmegaEstimator

public RiskenOmegaEstimator riskenOmegaEstimator()

Retrieve the Risken Omega Estimator

Returns:

The Risken Omega Estimator

pdfDot

public double pdfDot(RdProbabilityDensityFunction probabilityDensityFunction,
TimeRdVertex timeRdVertex)
              throws java.lang.Exception

Compute the Next Incremental Time Derivative of the PDF

Parameters:

probabilityDensityFunction - The PDF

timeRdVertex - The R^d Time Vertex

Returns:

Next Incremental Time Derivative of the PDF

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

temporalPDF

public RdProbabilityDensityFunction temporalPDF(RdToR1 intialProbabilityDensityFunction)

Compute the Temporal Probability Distribution Function, if any

Parameters:

intialProbabilityDensityFunction - The Initial Probability Density Function

Returns:

The Temporal Probability Distribution Function

steadyStatePDF

public RdToR1 steadyStatePDF()

Compute the Steady-State Probability Distribution Function, if any

Returns:

The Steady-State Probability Distribution Function