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Moments of passage time

We will use the matrices introduced above to derive $\mathbf{G}^{(\ell)}$ and $\mathbf{G}^{(\ell)}_r$ for $r=1,2,3$. We first derive those for the repeating part, $\mathbf{G} \equiv
\mathbf{G}^{(\hat{\ell})}$ and $\mathbf{G}_r \equiv
\mathbf{G}^{(\hat{\ell})}_r$. Then, $\mathbf{G}$ and $\mathbf{G}_r$ are used to derive those for the nonrepeating part, $\mathbf{G}^{(\ell)}$ and $\mathbf{G}^{(\ell)}_r$ for $1\leq \ell<\hat{\ell}$.


Takayuki Osogami 2005-07-19