How to "properly" handle incorrect values in a random walk? I'm performing a simple one dimensional walk to create sample interest rates. Whilst I know there are lots of options for encouraging values to oscillate around a mean etc. I'm yet to find a simple "proper" way to handle truly random processes going out of bounds. Whilst you could simply turn it in the other direction, is there some sort of commonly accepted way of making asymptotically less and less likely to get closer to the boundary the closer you get to it?
A random walk $(X_i)$ can't become negative if there are no positive-probability transitions to negative values. One condition that causes it to stay finite with probability&nbsp;$1$ is that, for all large enough $n$, $\mathbb{E}(X_{i+1}|X_i=n)&lt;n$.