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I believe that the process you postulate has a Beta conditional distribution. If my memory serves me well, I have encountered it in the book by Liptser and Shiryayev "Statistics of Random Processes" as the evolution of the conditional probability in a HMM. This was 10+ years ago, therefore I might be well off. In that case you should be sampling from Beta ...

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You are not going to get a process which stays within bounds if your increments are normal random variables, which have an unbounded distribution. You probably want to look at some kind of random walk, where the increment is a discrete distribution. In other words you have a finite list of values which you add or subtract, each with a positive probability. ...

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I assume that this decomposition is possible in the case of a variance swap as variance is decomposable in the sense that $$V = VAR(R_1+ \cdots + R_N) \approx \frac1N \sum_{i=1}^N R_i^2 .$$ This for any $n \le N$ we can write  V \approx \frac1N \sum_{i=1}^n R_i^2 + \frac1N \sum_{i=n+1}^N R_i^2 = \frac n N \frac1n \sum_{i=1}^n R_i^2 + \frac{N-n}{N} ...

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