version 4.2

Author: ac-guidoum

DESCRIPTION

@@ -1,7 +1,7 @@
 Package: Sim.DiffProc
 Type: Package
 Version: 4.2
-Date: 2018-10-17
+Date: 2018-10-18
 Title: Simulation of Diffusion Processes
 Authors@R: c(
     person("Arsalane Chouaib", "Guidoum",

README.md

@@ -11,7 +11,7 @@
 [![minimal R version](https://img.shields.io/badge/R%3E%3D-2.15.1-blue.svg?style=flat-plastic)](https://cran.r-project.org/) 
 
 ------------------------------------------------------------------------
-![Github](https://img.shields.io/badge/Github-4.2(at:2018.10.17)-blue.svg)
+![Github](https://img.shields.io/badge/Github-4.2(at:2018.10.18)-blue.svg)
 ![](http://www.r-pkg.org/badges/version-last-release/Sim.DiffProc?color=blue) [![Rdoc](http://www.rdocumentation.org/badges/version/Sim.DiffProc)](http://www.rdocumentation.org/packages/Sim.DiffProc)
 
 

inst/NEWS.Rd

@@ -4,7 +4,7 @@
 
 \section{CHANGES IN \pkg{Sim.DiffProc} VERSION 4.2}{
     \itemize{
-	  \item{Release date: 2018-10-17.}
+	  \item{Release date: 2018-10-18.}
       \item{Manual update.}
       \item{Minor bug fixes: R (>= 3.5.0).}
     }

inst/doc/bridgesde.Rmd

@@ -74,12 +74,12 @@ Assume that we want to describe the following bridge sde in It
 \begin{equation}\label{eq0166}
 dX_t = \frac{1-X_t}{1-t} dt + X_t dW_{t},\quad X_{t_{0}}=3 \quad\text{and}\quad X_{T}=1
 \end{equation}
-We simulate a flow of $5000$ trajectories, with integration step size $\Delta t = 0.001$, and $x_0 = 3$ at time $t_0 = 0$, $y = 1$ at terminal time $T=1$.
+We simulate a flow of $1000$ trajectories, with integration step size $\Delta t = 0.001$, and $x_0 = 3$ at time $t_0 = 0$, $y = 1$ at terminal time $T=1$.
 
 ```{r}
 f <- expression((1-x)/(1-t))
 g <- expression(x)
-mod <- bridgesde1d(drift=f,diffusion=g,x0=3,y=1,M=5000,method="milstein")
+mod <- bridgesde1d(drift=f,diffusion=g,x0=3,y=1,M=1000,method="milstein")
 mod
 summary(mod) ## default: summary at time = (T-t0)/2
 ```
@@ -179,12 +179,12 @@ dY_t = -(1+X_{t}) Y_{t} dt +  0.1 (1-X_{t}) \circ dW_{2,t},\quad Y_{t_{0}}=-0.5
 \end{cases}
 \end{equation}
 
-We simulate a flow of $5000$ trajectories, with integration step size $\Delta t = 0.01$, and using Runge-Kutta method order 1:
+We simulate a flow of $1000$ trajectories, with integration step size $\Delta t = 0.01$, and using Runge-Kutta method order 1:
 
 ```{r}
 fx <- expression(-(1+y)*x , -(1+x)*y)
 gx <- expression(0.2*(1-y),0.1*(1-x))
-mod2 <- bridgesde2d(drift=fx,diffusion=gx,x0=c(1,-0.5),y=c(1,0.5),Dt=0.01,M=5000,type="str",method="rk1")
+mod2 <- bridgesde2d(drift=fx,diffusion=gx,x0=c(1,-0.5),y=c(1,0.5),Dt=0.01,M=1000,type="str",method="rk1")
 mod2
 summary(mod2) ## default: summary at time = (T-t0)/2
 ```
@@ -297,12 +297,12 @@ dZ_t = 4 (1-Z_{t}) Y_{t} dt + 0.2 dW_{3,t},\quad Z_{t_{0}}=0.5 \quad\text{and}\q
 \end{cases}
 \end{equation}
 
-We simulate a flow of $5000$ trajectories, with integration step size $\Delta t = 0.001$.
+We simulate a flow of $1000$ trajectories, with integration step size $\Delta t = 0.001$.
 
 ```{r}
 fx <- expression(-4*(1+x)*y, 4*(1-y)*x, 4*(1-z)*y)
 gx <- rep(expression(0.2),3)
-mod3 <- bridgesde3d(x0=c(0,-1,0.5),y=c(0,-2,0.5),drift=fx,diffusion=gx,M=5000)
+mod3 <- bridgesde3d(x0=c(0,-1,0.5),y=c(0,-2,0.5),drift=fx,diffusion=gx,M=1000)
 mod3
 summary(mod3) ## default: summary at time = (T-t0)/2
 ```

inst/doc/bridgesde.html

@@ -1,5 +1,5 @@
 ---
-title: "Parametric Estimation of 1-D Stochastic Differential Equation"
+title: "Parametric Estimation of 1-D Stochastic Differential Equation" 
 author: 
 - A.C. Guidoum^[Department of Probabilities & Statistics, Faculty of Mathematics, University of Science and Technology Houari Boumediene, BP 32 El-Alia, U.S.T.H.B, Algeria, E-mail  ([email protected])] and K. Boukhetala^[Faculty of Mathematics, University of Science and Technology Houari Boumediene, BP 32 El-Alia, U.S.T.H.B, Algeria, E-mail ([email protected])]
 date: "`r Sys.Date()`"

inst/doc/fitsde.Rmd

@@ -91,7 +91,7 @@ Set the model $X_t$:
 ```{r}
 f <- expression( (1-0.5*x) )
 g <- expression( 1 )
-mod1d <- snssde1d(drift=f,diffusion=g,x0=1.7,M=10000,method="taylor")
+mod1d <- snssde1d(drift=f,diffusion=g,x0=1.7,M=1000,method="taylor")
 ```
 Generate the first-passage-time $\tau_{S(t)}$, with `fptsde1d()` function ( based on `density()` function in [base] package):
 ```{r}
@@ -166,7 +166,7 @@ Using `fptsde1d()` and `dfptsde1d()` functions in the [Sim.DiffProc](https://cra
 ## Set the model X(t)
 f <- expression( 0.48*x )
 g <- expression( 0.07*x )
-mod1 <- snssde1d(drift=f,diffusion=g,x0=1,T=10,M=10000)
+mod1 <- snssde1d(drift=f,diffusion=g,x0=1,T=10,M=1000)
 ## Set the boundary S(t)
 St  <- expression( 7 + 3.2 * t + 1.4 * t * sin(1.75 * t) )
 ## Generate the fpt
@@ -212,7 +212,7 @@ Using `fptsde1d()` and `dfptsde1d()` functions in the [Sim.DiffProc](https://cra
 theta1=0.5
 f <- expression( theta1*x*(10+0.2*sin(2*pi*t)+0.3*sqrt(t)*(1+cos(3*pi*t))-x) )
 g <- expression( sqrt(0.1)*x )
-mod2 <- snssde1d(drift=f,diffusion=g,x0=8,t0=1,T=4,M=10000)
+mod2 <- snssde1d(drift=f,diffusion=g,x0=8,t0=1,T=4,M=1000)
 ## Set the boundary S(t)
 St  <- expression( 12 )
 ## Generate the fpt
@@ -279,7 +279,7 @@ Set the system $(X_t , Y_t)$:
 ```{r}
 fx <- expression(5*(-1-y)*x , 5*(-1-x)*y)
 gx <- expression(0.5*y,0.5*x)
-mod2d <- snssde2d(drift=fx,diffusion=gx,x0=c(x=1,y=-1),M=10000,type="str")
+mod2d <- snssde2d(drift=fx,diffusion=gx,x0=c(x=1,y=-1),M=1000,type="str")
 ```
 Generate the couple \((\tau_{(S(t),X_{t})},\tau_{(S(t),Y_{t})})\), with `fptsde2d()` function::
 ```{r}
@@ -396,7 +396,7 @@ Set the system $(X_t , Y_t , Z_t)$:
 ```{r}
 fx <- expression(4*(-1-x)*y , 4*(1-y)*x , 4*(1-z)*y) 
 gx <- rep(expression(0.2),3)
-mod3d <- snssde3d(drift=fx,diffusion=gx,x0=c(x=2,y=-2,z=0),M=10000)
+mod3d <- snssde3d(drift=fx,diffusion=gx,x0=c(x=2,y=-2,z=0),M=1000)
 ```
 Generate the triplet $(\tau_{(S(t),X_{t})},\tau_{(S(t),Y_{t})},\tau_{(S(t),Z_{t})})$, with `fptsde3d()` function::
 ```{r}

inst/doc/fitsde.html

@@ -69,24 +69,13 @@ sde.fun1d <- function(data, i){
      return(c(mean(d),var(d)))
 }
 # Parallel MOnte Carlo for mod1
-mcm.mod1 = MCM.sde(model=mod1,statistic=sde.fun1d,R=100, exact=list(m=E.mod1(1),S=V.mod1(1)),parallel="snow",ncpus=2)
+mcm.mod1 = MCM.sde(model=mod1,statistic=sde.fun1d,R=10, exact=list(m=E.mod1(1),S=V.mod1(1)),parallel="snow",ncpus=2)
 mcm.mod1
 # Parallel MOnte Carlo for mod2
-mcm.mod2 = MCM.sde(model=mod2,statistic=sde.fun1d,R=100, exact=list(m=E.mod2(1),S=V.mod2(1)),parallel="snow",ncpus=2)
+mcm.mod2 = MCM.sde(model=mod2,statistic=sde.fun1d,R=10, exact=list(m=E.mod2(1),S=V.mod2(1)),parallel="snow",ncpus=2)
 mcm.mod2
 ```
 
-```{r,fig.cap=' MC output of mean and variance of `mod1`', fig.env='figure*'}
-# plot(s) of Monte Carlo outputs of mod1
-plot(mcm.mod1,index = 1)  # mean
-plot(mcm.mod1,index = 2)  # variance
-```
-
-```{r,fig.cap=' MC output of mean and variance of `mod2`', fig.env='figure*'}
-# plot(s) of Monte Carlo outputs of mod2
-plot(mcm.mod2,index = 1)  # mean
-plot(mcm.mod2,index = 2)  # variance
-```
 
 ## Two-dimensional SDEs
 
@@ -109,7 +98,7 @@ sde.fun2d <- function(data, i){
   return(c(mean(d$x),mean(d$y),var(d$x),var(d$y),cov(d$x,d$y)))
 }
 ## Parallel Monte-Carlo of 'OUI' at time 10
-mcm.mod2d = MCM.sde(OUI,statistic=sde.fun2d,time=10,R=100,exact=tvalue,parallel="snow",ncpus=2)
+mcm.mod2d = MCM.sde(OUI,statistic=sde.fun2d,time=10,R=10,exact=tvalue,parallel="snow",ncpus=2)
 mcm.mod2d
 ```
 
@@ -126,7 +115,7 @@ sde.fun3d <- function(data, i){
   return(c(mean(d$x),median(d$x),Mode(d$x),var(d$x),cov(d$x,d$y),cov(d$x,d$z)))
 }
 ## Monte-Carlo at time = 10
-mcm.mod3d = MCM.sde(modtra,statistic=sde.fun3d,R=100,parallel="snow",ncpus=2)
+mcm.mod3d = MCM.sde(modtra,statistic=sde.fun3d,R=10,parallel="snow",ncpus=2)
 mcm.mod3d
 ```