Interpreting the Minimum-Time Term in Vasicek Covariance Integrals

Summary

The document clarifies the notation u∧t that appears in a covariance integral while deriving the Vasicek model. It means the minimum of the two arguments: for example, when s is earlier than t, s∧t equals s. This is the same minimum-time structure used in the covariance of Brownian motion.

The exchange provides a notation-level explanation and points to Brownian-motion covariance as the relevant background for evaluating such expressions. It does not work through the integral, derive the Vasicek result, or give a numerical example. Readers still need the surrounding model setup and integration steps to complete the derivation.

Key ideas

• The symbol u∧t denotes the smaller of u and t.
• When s<t, the minimum s∧t is s.
• The same minimum-time notation appears in Brownian-motion covariance expressions.
• The answer explains the notation but does not evaluate the full Vasicek integral.

Tags

# Help evaluating covariance integral when deriving vasiceks model


# Help evaluating covariance integral when deriving vasiceks model












Im working through a solution to evaluating pricing for Vasiceks model

However i dont understand the u∧t terms and how that behaves under the integrals...any help??

Cheers

## Answer by Toofreak (score 2)

https://quant.stackexchange.com/a/41139

that symbol means "the min of". So for example, if: $s<t$, then $s$ ^ t = s.

If you look in any book for the Covariance of a BM, you will see that same symbol and how to work with it. Cheers.

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