R1FokkerPlanckOrnsteinUhlenbeck

java.lang.Object

org.drip.dynamics.kolmogorov.R1FokkerPlanck

org.drip.dynamics.kolmogorov.R1FokkerPlanckCKLS

org.drip.dynamics.kolmogorov.R1FokkerPlanckOrnsteinUhlenbeck

public class R1FokkerPlanckOrnsteinUhlenbeck
extends R1FokkerPlanckCKLS

R1FokkerPlanckOrnsteinUhlenbeck exposes the R¹ Ornstein-Uhlenbeck 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

R1FokkerPlanckOrnsteinUhlenbeck(CKLSParameters cklsParameters)
R1FokkerPlanckOrnsteinUhlenbeck Constructor

Method Summary

Modifier and Type	Method	Description
`R1ProbabilityDensityFunction`	`deltaStartTemporalPDF(double xDeltaAnchor)`	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
- R1FokkerPlanckOrnsteinUhlenbeck
  
  public R1FokkerPlanckOrnsteinUhlenbeck(CKLSParameters cklsParameters) throws java.lang.Exception
  
  R1FokkerPlanckOrnsteinUhlenbeck 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 xDeltaAnchor)
  
  Description copied from class: R1FokkerPlanck
  
  Compute the Temporal Probability Distribution Function given the Delta 0 Starting PDF
  
  Overrides:
  
  deltaStartTemporalPDF in class R1FokkerPlanck
  
  Parameters:
  
  xDeltaAnchor - The X Anchor for the Delta Function
  
  Returns:
  
  The Temporal Probability Distribution Function given the Delta 0 Starting PDF