Package org.drip.dynamics.kolmogorov

Class R1FokkerPlanck

java.lang.Object

org.drip.dynamics.kolmogorov.R1FokkerPlanck

Direct Known Subclasses:

R1FokkerPlanckBrownian, R1FokkerPlanckCKLS

public class R1FokkerPlanck
extends java.lang.Object

R1FokkerPlanck exposes the R¹ 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
R1FokkerPlanck(R1ToR1Drift driftFunction, R1ToR1Volatility volatilityFunction)	R1FokkerPlanck Constructor

Method Summary

Modifier and Type	Method	Description
R1ProbabilityDensityFunction	deltaStartTemporalPDF(double x0)	Compute the Temporal Probability Distribution Function given the Delta 0 Starting PDF
R1ToR1Drift	driftFunction()	Retrieve the Drift Function
double	pdfDot(R1ProbabilityDensityFunction probabilityDensityFunction, TimeR1Vertex timeR1Vertex)	Compute the Next Incremental Time Derivative of the PDF
R1ToR1	steadyStatePDF()	Compute the Steady-State Probability Distribution Function, if any
R1ProbabilityDensityFunction	temporalPDF(R1ToR1 intialProbabilityDensityFunction)	Compute the Temporal Probability Distribution Function, if any
R1ToR1Volatility	volatilityFunction()	Retrieve the Volatility Function

Methods inherited from class java.lang.Object

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

Constructor Details

R1FokkerPlanck

public R1FokkerPlanck(R1ToR1Drift driftFunction,
R1ToR1Volatility volatilityFunction)
               throws java.lang.Exception

R1FokkerPlanck Constructor

Parameters:

driftFunction - The Drift Function

volatilityFunction - The Volatility Function

Throws:

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

Method Details

driftFunction

public R1ToR1Drift driftFunction()

Retrieve the Drift Function

Returns:

The Drift Function

volatilityFunction

public R1ToR1Volatility volatilityFunction()

Retrieve the Volatility Function

Returns:

The Volatility Function

pdfDot

public double pdfDot(R1ProbabilityDensityFunction probabilityDensityFunction,
TimeR1Vertex timeR1Vertex)
              throws java.lang.Exception

Compute the Next Incremental Time Derivative of the PDF

Parameters:

probabilityDensityFunction - The PDF

timeR1Vertex - The R¹ Time Vertex

Returns:

Next Incremental Time Derivative of the PDF

Throws:

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

temporalPDF

public R1ProbabilityDensityFunction temporalPDF(R1ToR1 intialProbabilityDensityFunction)

Compute the Temporal Probability Distribution Function, if any

Parameters:

intialProbabilityDensityFunction - The Initial Probability Density Function

Returns:

The Temporal Probability Distribution Function

steadyStatePDF

public R1ToR1 steadyStatePDF()

Compute the Steady-State Probability Distribution Function, if any

Returns:

The Steady-State Probability Distribution Function

deltaStartTemporalPDF

public R1ProbabilityDensityFunction deltaStartTemporalPDF(double x0)

Compute the Temporal Probability Distribution Function given the Delta 0 Starting PDF

Parameters:

x0 - The X Anchor for the Delta Function

Returns:

The Temporal Probability Distribution Function given the Delta 0 Starting PDF