Package org.drip.dynamics.kolmogorov

Class R1FokkerPlanckCIR

java.lang.Object

org.drip.dynamics.kolmogorov.R1FokkerPlanck

org.drip.dynamics.kolmogorov.R1FokkerPlanckCKLS

org.drip.dynamics.kolmogorov.R1FokkerPlanckCIR

public class R1FokkerPlanckCIR
extends R1FokkerPlanckCKLS

R1FokkerPlanckCIR exposes the R¹ Cox-Ingersoll-Ross 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
R1FokkerPlanckCIR(CKLSParameters cklsParameters)	R1FokkerPlanckCIR Constructor

Method Summary

Modifier and Type	Method	Description
R1ProbabilityDensityFunction	deltaStartTemporalPDF(double r0)	Compute the Temporal Probability Distribution Function given the Delta 0 Starting PDF
R1ToR1	steadyStatePDF()	Compute the Steady-State Probability Distribution Function, if any

Methods inherited from class org.drip.dynamics.kolmogorov.R1FokkerPlanckCKLS

cklsParameters

Methods inherited from class org.drip.dynamics.kolmogorov.R1FokkerPlanck

driftFunction, pdfDot, temporalPDF, volatilityFunction

Methods inherited from class java.lang.Object

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

Constructor Details

R1FokkerPlanckCIR

public R1FokkerPlanckCIR(CKLSParameters cklsParameters)
                  throws java.lang.Exception

R1FokkerPlanckCIR Constructor

Parameters:

cklsParameters - The CKLS Parameters

Throws:

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

Method Details

steadyStatePDF

public R1ToR1 steadyStatePDF()

Description copied from class: R1FokkerPlanck

Compute the Steady-State Probability Distribution Function, if any

Overrides:

steadyStatePDF in class R1FokkerPlanck

Returns:

The Steady-State Probability Distribution Function

deltaStartTemporalPDF

public R1ProbabilityDensityFunction deltaStartTemporalPDF(double r0)

Description copied from class: R1FokkerPlanck

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

Overrides:

deltaStartTemporalPDF in class R1FokkerPlanck

Parameters:

r0 - The X Anchor for the Delta Function

Returns:

The Temporal Probability Distribution Function given the Delta 0 Starting PDF