Brownian Slow Points: The Critical Case
Davis, Burgess ; Perkins, Edwin
Ann. Probab., Tome 13 (1985) no. 4, p. 779-803 / Harvested from Project Euclid
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It is known that if $B_t$ is a standard Wiener process then $\sup_t\lim \inf_{h\rightarrow 0+}(B_{t + h} - B_t)h^{-1/2} = 1 a.s.$ Here this is sharpened to $P(\exists t: \lim \inf_{h\rightarrow 0+}(B_{t+h} - B_t)h^{-1/2} = 1) = 1$, and $P(\exists t: B_{t + h} - B_t \geq h^{1/2}\forall h \in (0, \alpha)$ for some $\alpha > 0) = 0$. A number of other theorems of the same flavor are proved. Our results for the critical case for slow points are not as complete as the above.
Publié le : 1985-08-14
Classification:  Brownian motion paths,  local properties,  60G17,  60J65,  60G40 
@article{1176992908,
     author = {Davis, Burgess and Perkins, Edwin},
     title = {Brownian Slow Points: The Critical Case},
     journal = {Ann. Probab.},
     volume = {13},
     number = {4},
     year = {1985},
     pages = { 779-803},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992908}
}

Davis, Burgess; Perkins, Edwin. Brownian Slow Points: The Critical Case. Ann. Probab., Tome 13 (1985) no. 4, pp.  779-803. http://gdmltest.u-ga.fr/item/1176992908/