Martingale = Independent Increments?

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    Independent martingale
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SUMMARY

The discussion clarifies that for a Gaussian process, the properties of independent increments and having zero expectation are not equivalent. Specifically, increments can be independent without necessarily having a zero expectation. The conversation centers around the nuances of centered Gaussian processes, emphasizing the importance of understanding these distinctions in stochastic processes.

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  • Understanding of Gaussian processes
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  • Familiarity with the concept of independent increments
  • Basic grasp of statistical expectations
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Palindrom
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Here's a stupid question: for a Gaussian process, are these two properties equivalent?
 
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No - the increments can be independent without having zero expectation, and vice-versa.
 
Right, thank you, I have a centered Gaussian process in mind (should've mentioned it).
 

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