Add to ORKGIt is well-known (see Dvoretzky, Erd{\H o}s and Kakutani [8] and Le Gall [12]) that a planar Brownian motion $(B_t)_{t\ge 0}$ has points of infinite multiplicity, and these points form a dense set on the range. Our main result is the construction of a family of random measures, denoted by $\{{\mathcal M}_{\infty}^\alpha\}_{0< \alpha<2}$, that are supported by the set of the points of infinite multiplicity. We prove that for any $\alpha \in (0, 2)$, almost surely the Hausdorff dimension of ${\mathcal M}_{\infty}^\alpha$ equals $2-\alpha$, and ${\mathcal M}_{\infty}^\alpha$ is supported by the set of thick points defined in Bass, Burdzy and Khoshnevisan [1] as well as by that defined in De...
We investigate the Martin-L�of random sample paths of Brownian motion, applying techniques from algo...
By considering a counting-type argument on Brownian sample paths, we prove aresult similar to that o...
AbstractLet Xt be the Brownian motion in Rd. The random set Γ = {(t1,…, tn, z): Xtl = ··· = Xtn = z}...
In this version, we add the assumption \alpha_1+...+\alpha_p< 2 in Section 7.2, and fix some typos....
For each a [is an element of the set] (0, 1/2), there exists a random measure [beta] [subscript] a w...
We characterise the multiplicative chaos measure $\mathcal{M}$ associated to planar Brownian motion ...
[[abstract]]We propose a sufficient condition for a planar set to contain points of multiplicity c; ...
We use Girsanov's theorem to establish a conjecture of Khoshnevisan, Xiao and Zhong that ϕ(r)=rN−d/2...
In the paper, we study the existence of the local nondeterminism and the joint continuity of the loc...
We construct the analogue of Gaussian multiplicative chaos measures for the local times of planar Br...
Hausdorff measure is often used to measure fractal sets. However, there is a more natural quantity, ...
AbstractLet Jωx(t) = x + ∝0t bω(s) ds, where bω is planar Brownian motion starting at 0. A Wiener-ty...
AbstractConsider a planar Brownian motion run for finite time. Thefrontieror “outer boundary” of the...
Fine regularity of stochastic processes is usually measured in a local way by local Hölder...
After an introduction to Brownian motion, Hausdorff dimension, nonstandard analysis and Loeb measure...
We investigate the Martin-L�of random sample paths of Brownian motion, applying techniques from algo...
By considering a counting-type argument on Brownian sample paths, we prove aresult similar to that o...
AbstractLet Xt be the Brownian motion in Rd. The random set Γ = {(t1,…, tn, z): Xtl = ··· = Xtn = z}...
In this version, we add the assumption \alpha_1+...+\alpha_p< 2 in Section 7.2, and fix some typos....
For each a [is an element of the set] (0, 1/2), there exists a random measure [beta] [subscript] a w...
We characterise the multiplicative chaos measure $\mathcal{M}$ associated to planar Brownian motion ...
[[abstract]]We propose a sufficient condition for a planar set to contain points of multiplicity c; ...
We use Girsanov's theorem to establish a conjecture of Khoshnevisan, Xiao and Zhong that ϕ(r)=rN−d/2...
In the paper, we study the existence of the local nondeterminism and the joint continuity of the loc...
We construct the analogue of Gaussian multiplicative chaos measures for the local times of planar Br...
Hausdorff measure is often used to measure fractal sets. However, there is a more natural quantity, ...
AbstractLet Jωx(t) = x + ∝0t bω(s) ds, where bω is planar Brownian motion starting at 0. A Wiener-ty...
AbstractConsider a planar Brownian motion run for finite time. Thefrontieror “outer boundary” of the...
Fine regularity of stochastic processes is usually measured in a local way by local Hölder...
After an introduction to Brownian motion, Hausdorff dimension, nonstandard analysis and Loeb measure...
We investigate the Martin-L�of random sample paths of Brownian motion, applying techniques from algo...
By considering a counting-type argument on Brownian sample paths, we prove aresult similar to that o...
AbstractLet Xt be the Brownian motion in Rd. The random set Γ = {(t1,…, tn, z): Xtl = ··· = Xtn = z}...