There is [a question that was asked on stackoverflow](https://stackoverflow.com/questions/2441506/how-to-generate-correlated-binary-variables/2447678#2447678) that at first sounds simple but I think it's a lot harder than it sounds.

Suppose we have a stationary random process that generates a sequence of random variables x[i] where each *individual* random variable has a [Bernoulli distribution](http://en.wikipedia.org/wiki/Bernoulli_distribution) with probability p, but the correlation between any two of the random variables x[m] and x[n] is α|m-n|.

How is it possible to generate such a process? The textbook examples of a Bernoulli process (right distribution, but independent variables) and a discrete-time IID Gaussian process passed through a low-pass filter (right correlation, but wrong distribution) are very simple by themselves, but cannot be combined in this way... can they? Or am I missing something obvious? If you take a Bernoulli process and pass it through a low-pass filter, you no longer have a discrete-valued process.

(I can't create tags, so please retag as appropriate... stochastic-process?)