R Under development (unstable) (2025-12-12 r89163 ucrt) -- "Unsuffered Consequences"
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> library(Sim.DiffProc)
> 
> ## 2-dim SDE
> 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)
       x                 y          
 Min.   :-5.6639   Min.   : 0.4349  
 1st Qu.:-0.3902   1st Qu.: 1.7160  
 Median : 0.5497   Median : 2.4000  
 Mean   : 0.3265   Mean   : 2.7618  
 3rd Qu.: 1.2958   3rd Qu.: 3.3156  
 Max.   : 3.3886   Max.   :12.1161  
> 
> # Marginal density 
> 
> denM <- dsde2d(mod2d,pdf="M", at=0.5)
> denM

 Marginal density of X(t-t0)|X(t0)=1 at time t = 0.5

Data: x (1000 obs.);	Bandwidth 'bw' = 0.2844

       x                  f(x)           
 Min.   :-6.517219   Min.   :0.00002345  
 1st Qu.:-3.827439   1st Qu.:0.00869079  
 Median :-1.137660   Median :0.02711701  
 Mean   :-1.137660   Mean   :0.09276253  
 3rd Qu.: 1.552120   3rd Qu.:0.16197889  
 Max.   : 4.241899   Max.   :0.33562892  

 Marginal density of Y(t-t0)|Y(t0)=2 at time t = 0.5

Data: y (1000 obs.);	Bandwidth 'bw' = 0.2699

       y                   f(y)           
 Min.   :-0.3746588   Min.   :0.00001694  
 1st Qu.: 2.9504288   1st Qu.:0.00286031  
 Median : 6.2755165   Median :0.01451506  
 Mean   : 6.2755165   Mean   :0.07503885  
 3rd Qu.: 9.6006042   3rd Qu.:0.09181273  
 Max.   :12.9256919   Max.   :0.37303833  
> plot(denM)
> 
> # Joint density
> denJ <- dsde2d(mod2d,pdf="J", at= 0.5)
> denJ

 Joint density of (X(t-t0),Y(t-t0)|X(t0)=1,Y(t0)=2) at time t = 0.5

Data: (x,y) (2 x 1000 obs.);

       x                   y                  f(x,y)           
 Min.   :-5.663883   Min.   : 0.4349363   Min.   :0.000000000  
 1st Qu.:-3.400771   1st Qu.: 3.3552264   1st Qu.:0.000009329  
 Median :-1.137660   Median : 6.2755165   Median :0.000797373  
 Mean   :-1.137660   Mean   : 6.2755165   Mean   :0.008690271  
 3rd Qu.: 1.125452   3rd Qu.: 9.1958067   3rd Qu.:0.004050708  
 Max.   : 3.388564   Max.   :12.1160968   Max.   :0.148301896  
> plot(denJ)
> plot(denJ,display="contour")
> 
> proc.time()
   user  system elapsed 
   0.70    0.12    0.81