Why Uniform Distributions Are Sub-Gaussian

Summary

The document asks whether sub-Gaussian random variables or processes appear in financial models or applications, contrasting their rapidly decaying tails with the fat tails often seen in financial time series. The response offers one concise observation: a uniform distribution is sub-Gaussian, so sub-Gaussian variables do occur in principle.

This establishes a basic connection between a probability distribution and the sub-Gaussian class, but it does not describe a financial model, application, or trading method. It gives no supporting derivation, examples, or evidence about how useful the property is in practice. Readers should treat the reply as a narrow mathematical observation, not as a discussion of financial returns or a claim that market data are sub-Gaussian.

Key ideas

• A uniform random variable is an example of a sub-Gaussian variable.
• The response establishes possibility but gives no specific financial application.
• The document does not provide a model, derivation, or empirical evidence.

Tags

# sub-Gaussian random variables in financial economics


# sub-Gaussian random variables in financial economics












Unlike financial time series that typically possess fat tails, sub-Gaussian random variables have strong decay in the tails of their distribution. do sub-Gaussian random variables or processes appear in any finance models, or are they useful in financial applications somehow?

## Answer by Igor Rivin (score -1)

https://quant.stackexchange.com/a/59261

Since a uniform distribution is subgaussian, yes.

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