Stratonovich’s signatures of Brownian motion determine Brownian sample paths

Packing Measure of the Sample Paths of Fractional Brownian Motion

Let X(t) (t ∈ R) be a fractional Brownian motion of index α in Rd. If 1 < αd , then there exists a positive finite constant K such that with probability 1, φ-p(X([0, t])) = Kt for any t > 0 , where φ(s) = s 1 α /(log log 1 s ) 1 2α and φ-p(X([0, t])) is the φ-packing measure of X([0, t]).

Super-brownian Motion with Reflecting Historical Paths

We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results about path behavior for processes under any limit distribution. In p...

Super-Brownian motion with reflecting historical paths

Brownian Brownian Motion – I

A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work we study a 2D version of this model, where the molecule is a heavy disk of mass M ≫ 1 and the gas is represented by just one point particle of mass m = 1, which interacts with the disk and the walls of the container via elastic collisions. Chaotic behavior of...

Sample Path Properties of Bifractional Brownian Motion

Let B = { B(t), t ∈ R+ } be a bifractional Brownian motion in R. We prove that B is strongly locally nondeterministic. Applying this property and a stochastic integral representation of B , we establish Chung’s law of the iterated logarithm for B , as well as sharp Hölder conditions and tail probability estimates for the local times of B . We also consider the existence and the regularity of th...