Stochastic Differential Equation with positive-only noise?

This may be more of a math question, but are there methods available for solving stochastic differential equations with positive only noise? I’ve been tinkering around with an interesting scalar system that includes the usual Weiner process, but I’m interested in results where fluctuations can only be in the positive direction. I already started the tinkering in Julia, so I thought I would ask here. Any pointers appreciated!

Bounded noise cannot be an SDE, it is an RODE.

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