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dsantanu
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How to prove that two poisson processes can never be negatively correlated.
Correlation between poisoon processes
- Context: Graduate
- Thread starter dsantanu
- Start date
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- Correlation
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Discussion Overview
The discussion centers around the correlation properties of Poisson processes, specifically addressing whether two Poisson processes can be negatively correlated. Participants explore theoretical aspects and mathematical foundations related to this question.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant inquires about proving that two Poisson processes can never be negatively correlated.
- Another participant suggests using the Frechet bounds and the positivity of Poisson random variables as part of the proof.
- A participant expresses a lack of understanding regarding Frechet bounds, indicating their background in probability and mathematics but not in physics.
- It is mentioned that the result may be derived from copula theory, with a reference to a survey article by Embrechts that discusses relevant results.
- A later reply acknowledges the possibility that the initial conjecture may not be true, suggesting that a Poisson distribution with negative correlation could be constructed, which may extend to Poisson processes.
Areas of Agreement / Disagreement
Participants do not reach a consensus; there are competing views regarding the correlation of Poisson processes, with some suggesting it is impossible while others propose that negative correlation may be feasible.
Contextual Notes
Some assumptions about the definitions and properties of Poisson processes and distributions are not fully explored, leaving room for further clarification and discussion.