Prob/Stats Material on complex random variables and exotic probabilities

AI Thread Summary
The discussion centers on the search for books that specifically address complex random variables, particularly those that can take on complex values rather than just probabilities in the complex range. The interest stems from a desire to integrate knowledge of complex analysis with statistics. The inquiry also extends to exotic probabilities, including those that can be complex-valued, exceed 1, or even be negative. The participant notes that most existing literature is found in physics papers, particularly in the context of quantum physics, and expresses a preference for more mathematical treatments of these topics. A referenced Wikipedia page is mentioned as a potential resource, highlighting the relevance of complex random variables in signal processing.
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I am looking for books that have sections or even chapters devoted to complex random variables, or random variables that can take on complex values (NOT probabilities that are valued in the complex range, in this regard). On the other hand, if someone does know any books that contain material on exotic probabilities that would be neat too (in this case probability can be complex valued, greater than 1 or even negative). I got interested in this while brushing up on my complex analysis and reading a statistics book at the same time. Figured, why not try to combine the two in some way? I've seen other people have tried this, but most of the material I find are in physics papers and mostly are applied to quantum physics. If possible, I'd like to see more mathematical treatments of the topics. Thanks.
 
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