Plot correlation between two variables generating samples from conditional CDF

Hello all,

I'm trying to understand the correlation between dependent variables Y_(n+1) and Y_(n) and was thinking of plotting the pair (Y_(n)m Y_(n+1)). I have a complicated CDF which looks like:

P(Y_(n+1) <= y | Y_(n) = y_(n) ) = h(y)* exp(g(y)*m(y_(n)))

where h, g, m are some functions. In order to plot the correlation, I would require sample pairs (Y_(n)m Y_(n+1)) generated from this conditional CDF. I was thinking of using inverse transform method to generate the samples but I'm facing two difficulties: first, assuming that I fix some arbitrary Y_(n), the CDF itself is complicated enough that obtaining a closed form won't be possible in which case, how can I numerically evaluate the inverse CDF and generate samples of Y_(n+1) for every fixed Y_(n). And secondly, I have a huge doubt on if this is the right way to generate samples in such a way. But, the final goal is to see the correlation between Y_(n+1) and Y_(n). Any simulation example showing this would be tremendously helpful.

Thanks a lot!