rsde2d {Sim.DiffProc} | R Documentation |
Transition density and random generation for the joint and marginal of (X(t-s),Y(t-s) | X(s)=x0,Y(s)=y0)
of the SDE's 2-d.
rsde2d(object, ...) dsde2d(object, ...) ## Default S3 method: rsde2d(object, at, ...) ## Default S3 method: dsde2d(object, pdf=c("Joint","Marginal"), at, ...) ## S3 method for class 'dsde2d' plot(x,display=c("persp","rgl","image","contour"),hist=FALSE,...)
object |
an object inheriting from class |
at |
time between |
pdf |
probability density function |
x |
an object inheriting from class |
display |
display plots. |
hist |
if |
... |
potentially potentially arguments to be passed to methods, such as |
The function rsde2d
returns a M
random variable x(t=at),y(t=at) realize at time t=at.
And dsde2d
returns a bivariate density approximation for (X(t-s),Y(t-s) | X(s)=x0,Y(s)=y0)
. with t=at is a fixed time between t0
and T
.
An overview of this package, see browseVignettes('Sim.DiffProc')
for more informations.
dsde2d
gives the bivariate density approximation for (X(t-s),Y(t-s) | X(s)=x0,Y(s)=y0)
.
rsde2d
generates random of the couple (X(t-s),Y(t-s) | X(s)=x0,Y(s)=y0)
.
A.C. Guidoum, K. Boukhetala.
kde2d
Two-dimensional kernel density estimation in "MASS" package.
kde
Kernel density estimate for 1- to 6-dimensional data in "ks" package.
sm.density
Nonparametric density estimation in one, two or three dimensions in "sm" package.
rng
random number generators in "yuima" package.
BiGQD.density
Generate the transition density of a bivariate generalized quadratic diffusion model (2D GQD).
## Example:1 set.seed(1234) # SDE's 2d fx <- expression(3*(2-y),2*x) gx <- expression(1,y) mod2d <- snssde2d(drift=fx,diffusion=gx,x0=c(1,2),M=1000) # random r2d <- rsde2d(mod2d,at=0.5) summary(r2d) # Marginal density denM <- dsde2d(mod2d,pdf="M", at=0.5) denM plot(denM) # Joint density denJ <- dsde2d(mod2d,pdf="J",n=200, at= 0.5,lims=c(-3,4,0,6)) denJ plot(denJ) plot(denJ,display="contour") ## Example 2: Bivariate Transition Density of 2 Brownian motion (W1(t),W2(t)) in [0,1] ## Not run: B2d <- snssde2d(drift=rep(expression(0),2),diffusion=rep(expression(1),2), M=10000) for (i in seq(B2d$Dt,B2d$T,by=B2d$Dt)){ plot(dsde2d(B2d, at = i,lims=c(-3,3,-3,3),n=100), display="contour",main=paste0('Transition Density \n t = ',i)) } ## End(Not run) ## Example 3: ## Not run: fx <- expression(4*(-1-x)*y , 4*(1-y)*x ) gx <- expression(0.25*y,0.2*x) mod2d1 <- snssde2d(drift=fx,diffusion=gx,x0=c(x0=1,y0=-1), M=5000,type="str") # Marginal transition density for (i in seq(mod2d1$Dt,mod2d1$T,by=mod2d1$Dt)){ plot(dsde2d(mod2d1,pdf="M", at = i),main= paste0('Marginal Transition Density \n t = ',i)) } # Bivariate transition density for (i in seq(mod2d1$Dt,mod2d1$T,by=mod2d1$Dt)){ plot(dsde2d(mod2d1, at = i,lims=c(-1,2,-1,1),n=100), display="contour",main=paste0('Transition Density \n t = ',i)) } ## End(Not run) ## Example 4: Bivariate Transition Density of 2 bridge Brownian motion (W1(t),W2(t)) in [0,1] ## Not run: B2d <- bridgesde2d(drift=rep(expression(0),2), diffusion=rep(expression(1),2),M=5000) for (i in seq(0.01,0.99,by=B2d$Dt)){ plot(dsde2d(B2d, at = i,lims=c(-3,3,-3,3), n=100),display="contour",main= paste0('Transition Density \n t = ',i)) } ## End(Not run) ## Example 5: Bivariate Transition Density of bridge ## Ornstein-Uhlenbeck process and its integral in [0,5] ## dX(t) = 4*(-1-X(t)) dt + 0.2 dW1(t) ## dY(t) = X(t) dt + 0 dW2(t) ## x01 = 0 , y01 = 0 ## x02 = 0, y02 = 0 ## Not run: fx <- expression(4*(-1-x) , x) gx <- expression(0.2 , 0) OUI <- bridgesde2d(drift=fx,diffusion=gx,Dt=0.005,M=1000) for (i in seq(0.01,4.99,by=OUI$Dt)){ plot(dsde2d(OUI, at = i,lims=c(-1.2,0.2,-2.5,0.2),n=100), display="contour",main=paste0('Transition Density \n t = ',i)) } ## End(Not run)