# SDEsim2: A Simulated Non-Linear Bivariate Diffusion In DiffusionRgqd: Inference and Analysis for Generalized Quadratic Diffusions

## Description

The dataset contains discretely sampled observations for a simulated stochastic differential equation (SDE) with dynamics:

dX_t = 2.0(Y_t-X_t)dt+0.3sqrt(X_tY_t)dW_t

dY_t = 1.0(5-Y_t)dt+0.5sqrt(Y_t)dB_t

where `dW_t` and `dB_t` are standard Brownian motions, `t` is time and `X_0 = 5`, `Y_0 = 5`.

## Usage

 `1` ```data("SDEsim2") ```

## Format

A data frame with 801 observations on the following 3 variables.

`Xt`

Xt trajectory of the diffusion.

`Yt`

Yt trajectory of the diffusion.

`time`

Time vector (`time[i+1]-time[i] = 1/8`).

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ``` data(SDEsim2) data(SDEsim2) attach(SDEsim2) # Have a look at the time series: plot(Xt~time,type='l',col='blue',ylim=c(2,10),main='Simulated Data',xlab='Time (t)',ylab='State', axes=FALSE) lines(Yt~time,col='red') expr1=expression(dX[t]==2(Y[t]-X[t])*dt+0.3*sqrt(X[t]*Y[t])*dW[t]) expr2=expression(dX[t]==(5-Y[t])*dt+0.5*sqrt(Y[t])*dB[t]) text(50,9,expr1) text(50,8.5,expr2) axis(1,seq(0,100,5)) axis(1,seq(0,100,5/10),tcl=-0.2,labels=NA) axis(2,seq(0,20,2)) ```

### Example output

```Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE