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Exact value of mean reversion rate knowing terminal value of the process

Let you have the following mean reverting process: $\text{d}x_{t}=a(\theta-x_{t})\text{d}t$, where the diffusion term is absent, that is this process is not stochastic. Let you know the value of ...
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Mean Reverting Spread

I have constructed a mean reverting spread using two indexes. I know they have to be mean reverting, but when plotted side by side they are mean reverting for a little bit and then deviate and head ...