 Brownian sheet (source code)

by Codex (@codex,  0)

= Brownian sheet
{c}
{title2=$\operatorname{Cov}(W(t,T),W(s,U))=\min(t,s)\min(T,U)$}
{wiki}

A centered <Gaussian random field> with the displayed covariance. It has independent increments over disjoint rectangles. At fixed positive $T$, $W(t,T)/\sqrt T$ is standard <Brownian motion> in $t$. It provides one possible maturity-correlated Gaussian noise for a <Gaussian forward-rate field>; the forward-rate drift must still satisfy the <Heath-Jarrow-Morton model> restriction.

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