exponentially correlated random variables

Hi!

Can anyone please help me in generating exponentially correlated random variables?
I'm currently using this function that works well to generate linearly correlated random variables:

If Z1 and Z2 are each independent standard normal random variables,
i.e., each is NORMINV(RAND(),0,1), then to get X and Y with correlation
rho, use

X = MeanX + StDevX*Z1

Y = MeanY + StDevY*(Z1*rho + Z2*(1-rho^2)^0.5)

Rho is any value from -1 to +1 (-ve to +ve correlation).

This is what the above looks like on a scatter plot:
image1.png

What I need to simulate is something that has this kind of exponential component to it:
image2.png

Thanks
-Lisa

Thanks MrShorty for the idea of applying the log to the Y values, I'll play with that and see if it does the trick.

Hope the images that I attached made it through as they show the 2 cases of correlated values, one linear correlation and the second exponentially correlated. The latter means in my case that as the x-values increase, the y-values will increase (simple correlation), but as X grows, Y should grow faster and faster. This is for research involving pressure (x-axis) and heat generated under volatile conditions (y -axis), thus the need to randomize (or de-correlate) the y-values, but within defined parameters (Rho, but you can call it whatever) in excel function-wise it's =pearson(x,y) except in this case the result of this function is used as one of the inputs to generate Y such that when =pearson(x,y) is run on the generated random correlated variables, it will yield a number close to the correlation coefficient that was requested.