Material on complex random variables and exotic probabilities

In summary, the conversation discusses the search for books on complex random variables and exotic probabilities. The individual is interested in combining complex analysis and statistics, but is having trouble finding mathematical treatments on the topic. They mention that complex random variables are often used in signal processing and provide a link to a relevant Wikipedia page with references.
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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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  • #2

1. What are complex random variables?

Complex random variables are mathematical objects that represent the outcomes of random processes in a complex plane. They are typically used to model systems with both real and imaginary components, such as in electrical engineering and signal processing.

2. How are complex random variables different from real random variables?

Complex random variables have both real and imaginary components, while real random variables only have real components. This means that complex random variables can have more complex and diverse distributions, and require different mathematical tools for analysis.

3. What are exotic probabilities?

Exotic probabilities refer to probabilities that do not follow the standard laws of probability, such as the law of large numbers or the central limit theorem. These probabilities are often used in complex systems and can lead to unexpected and counterintuitive results.

4. How are exotic probabilities used in material on complex random variables?

Exotic probabilities are often used to model complex systems with multiple random variables, such as in quantum mechanics or financial markets. They allow for a more accurate representation of these systems and can provide insights into their behavior and outcomes.

5. What are some real-world applications of material on complex random variables and exotic probabilities?

The material on complex random variables and exotic probabilities has a wide range of applications, including in physics, engineering, finance, and statistics. Some examples include modeling quantum systems, analyzing financial markets, and predicting the behavior of complex systems in biology and social sciences.

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