On short-time asymptotics of one-dimensional Harris flows

Details On short-time asymptotics of one-dimensional Harris flows On short-time asymptotics of one-dimensional Harris flows

2010-10-26

arxiv.org/abs/1010.5349v1

Mathematics

Probability

15 pages, 1 figure

Scientific paper

We study the short-time asymptotical behavior of stochastic flows on \mathbb{R} in the \sup-norm. The results are stated in terms of a Gaussian process associated with the covariation of the flow. In case the Gaussian process has a continuous version the two processes can be coupled in such a way that the difference is uniformly $o(\ln\ln t^{-1})$. In case it has no continuous version, an $O(\ln\ln t^{-1})$ estimate is obtained under mild regularity assumptions. The main tools are Gaussian measure concentration and a martingale version of the Slepian comparison principle.

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