A CLT FOR THE L-2 MODULUS OF CONTINUITY OF BROWNIAN LOCAL TIME

作者：Chen Xia^*; Li Wenbo V; Marcus Michael B; Rosen Jay

来源：Annals of Probability, 2010, 38(1): 396-438.

DOI：10.1214/09-AOP486

• CLT
• Brownian local times
• modulus of continuity

Let {L-t(x); (x, t) is an element of R-1 x R-+(1)} denote the local time of Brownian motion, and
alpha(t) := integral(infinity)(-infinity)(L-t(x))(2)dx.
Let eta = N(0, 1) be independent of alpha(t). For each fixed t,
integral(infinity)(-infinity)(L-t(x+h) - L-t(x))(2) dx - 4ht/h(3/2) L -> (64/3)(1/2) root alpha(t)eta
as h -> 0. Equivalently,
integral(infinity)(-infinity)(L-t(x+1) - L-t(x))(2) dx - 4t/t(3/4) L -> (64/3)(1/2) root alpha(1)eta
as t -> infinity.

• 出版日期2010-1