On the Hausdorff Dimension of the Set Generated by Exceptional Oscillations of a Two-Parameter Wiener Process

S. Orey and S. J. Taylor (1974, Proc. London Math. Soc.28, 174-192) proved that for 0[less-than-or-equals, slant][lambda][less-than-or-equals, slant]1 the set E([lambda])={t[set membership, variant][0, 1] : lim suph[downwards arrow]0(2h log(1/h))-1/2 (W'(t+h)-W'(t))[greater-or-equal, slanted][lambda]} has Hausdorff dimension dim E([lambda])=1-[lambda]2 a.s. where W'(t) is a standard Wiener process. A corresponding result is obtained when W' is replaced by a two-parameter Wiener process.