# Simulation of Diffusion Processes

## Documentation for package ‘Sim.DiffProc’ version 2.2

- DESCRIPTION file.
- Overview of user guides and package vignettes; browse directory.
- Code demos. Use demo() to run them.
- Package NEWS.

## Help Pages

A B C D F G H I J K M O P R S T W

Sim.DiffProc-package | Simulation of Diffusion Processes.

## -- A --

ABM | Creating Arithmetic Brownian Motion Model
ABMF | Creating Flow of The Arithmetic Brownian Motion Model
Ajdbeta | Adjustment By Beta Distribution
Ajdchisq | Adjustment By Chi-Squared Distribution
Ajdexp | Adjustment By Exponential Distribution
Ajdf | Adjustment By F Distribution
Ajdgamma | Adjustment By Gamma Distribution
Ajdlognorm | Adjustment By Log Normal Distribution
Ajdnorm | Adjustment By Normal Distribution
Ajdt | Adjustment By Student t Distribution
Ajdweibull | Adjustment By Weibull Distribution
AnaSimFPT | Simulation The First Passage Time FPT For A Simulated Diffusion Process
AnaSimX | Simulation M-Samples of Random Variable X(v[t]) For A Simulated Diffusion Process
Appdcon | Approximated Conditional Law a Diffusion Process
Asys | Evolution a Telegraphic Process in Time

## -- B --

BB | Creating Brownian Bridge Model
BBF | Creating Flow of Brownian Bridge Model
Besselp | Creating Bessel process (by Milstein Scheme)
BMcov | Empirical Covariance for Brownian Motion
BMinf | Brownian Motion Property
BMIrt | Brownian Motion Property (Invariance by reversal of time)
BMIto1 | Properties of the stochastic integral and Ito Process [1]
BMIto2 | Properties of the stochastic integral and Ito Process [2]
BMItoC | Properties of the stochastic integral and Ito Process [3]
BMItoP | Properties of the stochastic integral and Ito Process [4]
BMItoT | Properties of the stochastic integral and Ito Process [5]
BMN | Creating Brownian Motion Model (by the Normal Distribution)
BMN2D | Simulation Two-Dimensional Brownian Motion (by the Normal Distribution)
BMN3D | Simulation Three-Dimensional Brownian Motion (by the Normal Distribution)
BMNF | Creating Flow of Brownian Motion (by the Normal Distribution)
BMP | Brownian Motion Property (trajectories brownian between function (+/-)2*sqrt(C*t))
BMRW | Creating Brownian Motion Model (by a Random Walk)
BMRW2D | Simulation Two-Dimensional Brownian Motion (by a Random Walk)
BMRW3D | Simulation Three-Dimensional Brownian Motion (by a Random Walk)
BMRWF | Creating Flow of Brownian Motion (by a Random Walk)
BMscal | Brownian Motion Property (Invariance by scaling)
BMStra | Stratonovitch Integral [1]
BMStraC | Stratonovitch Integral [2]
BMStraP | Stratonovitch Integral [3]
BMStraT | Stratonovitch Integral [4]

## -- C --

CEV | Creating Constant Elasticity of Variance (CEV) Models (by Milstein Scheme)
CIR | Creating Cox-Ingersoll-Ross (CIR) Square Root Diffusion Models (by Milstein Scheme)
CIRhy | Creating The modified CIR and hyperbolic Process (by Milstein Scheme)
CKLS | Creating The Chan-Karolyi-Longstaff-Sanders (CKLS) family of models (by Milstein Scheme)

## -- D --

DATA1 | Observation of Ornstein-Uhlenbeck Process
DATA2 | Observation of Geometric Brownian Motion Model
DATA3 | Observation of Arithmetic Brownian Motion
diffBridge | Creating Diffusion Bridge Models (by Euler Scheme)
DWP | Creating Double-Well Potential Model (by Milstein Scheme)

## -- F --

fctgeneral | Adjustment the Empirical Distribution of Random Variable X
fctrep_Meth | Calculating the Empirical Distribution of Random Variable X

## -- G --

GBM | Creating Geometric Brownian Motion (GBM) Models
GBMF | Creating Flow of Geometric Brownian Motion Models

## -- H --

hist_general | Adjustment the Density of Random Variable X by Histograms Methods
hist_meth | Histograms of Random Variable X
HWV | Creating Hull-White/Vasicek (HWV) Gaussian Diffusion Models
HWVF | Creating Flow of Hull-White/Vasicek (HWV) Gaussian Diffusion Models
Hyproc | Creating The Hyperbolic Process (by Milstein Scheme)
Hyprocg | Creating The General Hyperbolic Diffusion (by Milstein Scheme)

## -- I --

INFSR | Creating Ahn and Gao model or Inverse of Feller Square Root Models (by Milstein Scheme)
ItovsStra | Properties of the stochastic integral and Ito Process [1]
ItovsStraP | Properties of the stochastic integral and Ito Process [4]
ItovsStraT | Properties of the stochastic integral and Ito Process [5]

## -- J --

JDP | Creating The Jacobi Diffusion Process (by Milstein Scheme)

## -- K --

Kern_general | Adjustment the Density of Random Variable by Kernel Methods
Kern_meth | Kernel Density of Random Variable X

## -- M --

MartExp | Creating The Exponential Martingales Process

## -- O --

OU | Creating Ornstein-Uhlenbeck Process
OUF | Creating Flow of Ornstein-Uhlenbeck Process

## -- P --

PDP | Creating Pearson Diffusions Process (by Milstein Scheme)
PEABM | Parametric Estimation of Arithmetic Brownian Motion(Exact likelihood inference)
PEBS | Parametric Estimation of Model Black-Scholes (Exact likelihood inference)
PEOU | Parametric Estimation of Ornstein-Uhlenbeck Model (Exact likelihood inference)
PEOUexp | Parametric Estimation of Ornstein-Uhlenbeck Model (Explicit Estimators)
PEOUG | Parametric Estimation of Hull-White/Vasicek (HWV) Gaussian Diffusion Models(Exact likelihood inference)
PredCorr | Predictor-Corrector Method For One-Dimensional SDE
PredCorr2D | Predictor-Corrector Method For Two-Dimensional SDE
PredCorr3D | Predictor-Corrector Method For Three-Dimensional SDE

## -- R --

RadialP2D_1 | Two-Dimensional Attractive Model Model(S = 1,Sigma)
RadialP2D_1PC | Two-Dimensional Attractive Model in Polar Coordinates Model(S = 1,Sigma)
RadialP2D_2 | Two-Dimensional Attractive Model Model(S >= 2,Sigma)
RadialP2D_2PC | Two-Dimensional Attractive Model in Polar Coordinates Model(S >= 2,Sigma)
RadialP3D_1 | Three-Dimensional Attractive Model Model(S = 1,Sigma)
RadialP3D_2 | Three-Dimensional Attractive Model Model(S >= 2,Sigma)
RadialP_1 | Radial Process Model(S = 1,Sigma) Or Attractive Model
RadialP_2 | Radial Process Model(S >= 2,Sigma) Or Attractive Model
ROU | Creating Radial Ornstein-Uhlenbeck Process (by Milstein Scheme)

## -- S --

showData | Display a Data Frame in a Tk Text Widget
Sim.DiffProc | Simulation of Diffusion Processes.
snssde | Numerical Solution of One-Dimensional SDE
snssde2D | Numerical Solution of Two-Dimensional SDE
snssde3D | Numerical Solution of Three-Dimensional SDE
SRW | Creating Random Walk
Stgamma | Creating Stochastic Process The Gamma Distribution
Stst | Creating Stochastic Process The Student Distribution

## -- T --

Telegproc | Realization a Telegraphic Process
test_ks_dbeta | Kolmogorov-Smirnov Tests (Beta Distribution)
test_ks_dchisq | Kolmogorov-Smirnov Tests (Chi-Squared Distribution)
test_ks_dexp | Kolmogorov-Smirnov Tests (Exponential Distribution)
test_ks_df | Kolmogorov-Smirnov Tests (F Distribution)
test_ks_dgamma | Kolmogorov-Smirnov Tests (Gamma Distribution)
test_ks_dlognorm | Kolmogorov-Smirnov Tests (Log Normal Distribution)
test_ks_dnorm | Kolmogorov-Smirnov Tests (Normal Distribution)
test_ks_dt | Kolmogorov-Smirnov Tests (Student t Distribution)
test_ks_dweibull | Kolmogorov-Smirnov Tests (Weibull Distribution)
tho_02diff | Simulation The First Passage Time FPT For Attractive Model for Two-Diffusion Processes V(1) and V(2)
tho_M1 | Simulation The First Passage Time FPT For Attractive Model(S = 1,Sigma)
tho_M2 | Simulation The First Passage Time FPT For Attractive Model(S >= 2,Sigma)
TwoDiffAtra2D | Two-Dimensional Attractive Model for Two-Diffusion Processes V(1) and V(2)
TwoDiffAtra3D | Three-Dimensional Attractive Model for Two-Diffusion Processes V(1) and V(2)

## -- W --

WNG | Creating White Noise Gaussian