It is shown that the Ritz projection onto spaces of piecewise linear finite elements is bounded in the Sobolev space, $\overset {\circ} {W}_p^1$, for $2 \leqslant p \leqslant \infty$.

We study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log ...