I attempted to answer a question on dsp.stackexchange about the Cramér representation of wide-sense stationary discrete-time stochastic processes, and I failed to find any references that discuss the notion of absolute continuity of an orthogonal stochastic measure on $[0,2\pi)$ with respect to Lebesgue measure. I didn't even find anything that suggested an analogue of the Radon-Nikodym derivative for an orthogonal stochastic measure.
I took courses in measure-theoretic probability long ago, and I accept that there could very easily be an obvious answer that I fail to see.
- Is there an analogue of the Radon-Nikodym derivative for an orthogonal stochastic measure with respect to Lebesgue measure?
- If not, is there a way to explain why to someone in my situation?