The Hausdorff measure of the range of super-Brownian motion
ثبت نشده
چکیده
منابع مشابه
Brownian Motion and Hausdorff Dimension
In this paper, we develop Brownian motion and discuss its basic properties. We then turn our attention to the “size” of Brownian motion by defining Hausdorff dimension and its relationship to Brownian motion. This leads to the final result of the paper that for n ≥ 2, both the range and graph of Brownian motion have Hausdorff dimension 2.
متن کاملHausdorff Dimension and Its Applications
The theory of Hausdorff dimension provides a general notion of the size of a set in a metric space. We define Hausdorff measure and dimension, enumerate some techniques for computing Hausdorff dimension, and provide applications to self-similar sets and Brownian motion. Our approach follows that of Stein [4] and Peres [3].
متن کاملOn the boundary of the zero set of super-Brownian motion
If X(t, x) is the density of one-dimensional super-Brownian motion, we prove that dim(∂{x : X(t, x) > 0}) = 2 − 2λ0 ∈ (0, 1) a.s. on {Xt 6= 0}, where −λ0 ∈ (−1,−1/2) is the lead eigenvalue of a killed Ornstein-Uhlenbeck process. This confirms a conjecture of Mueller, Mytnik and Perkins [10] who proved the above with positive probability. To establish this result we derive some new basic propert...
متن کاملNonstandard Analysis, Fractal Properties and Brownian Motion
In this paper I explore a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the counting measure formulation of Lebesgue measure, I prove a nonstandard version of Frostman’s lemma and show that Hausdorff dimension can be computed through a counting argument rather than by taking the infimum of a sum of certain covers. This formulation is then applied to obtain a ...
متن کاملSome singular sample path properties of a multiparameter fractional Brownian motion
We prove a Chung-type law of the iterated logarithm for a multiparameter extension of the fractional Brownian motion which is not increment stationary. This multiparameter fractional Brownian motion behaves very differently at the origin and away from the axes, which also appears in the Hausdorff dimension of its range and in the measure of its pointwise Hölder exponents. A functional version o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998