No triple point of planar Brownian motion is accessible
نویسندگان
چکیده
منابع مشابه
No triple point of planar Brownian motion is accessible
We show that the boundary of a connected component of the complement of a planar Brownian path on a fixed time-interval contains almost surely no triple point of this Brownian path.
متن کاملExact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries
In this paper Lie symmetry analysis is applied to find new solution for Fokker Plank equation of geometric Brownian motion. This analysis classifies the solution format of the Fokker Plank equation.
متن کاملLogarithmic Potentials and Planar Brownian Motion
In Section 5, we saw that for a Brownian motion process in n _ 3 dimensions, P (limtxIX, = o0) = 1 for all x. In sharp contrast to this situation, a planar Brownian motion is certain to hit any nonpolar set. THEOREM 8.1. Let B be a Borel set. Then PX(VB < cX) is either identically 1 or identically 0. PROOF. A simple computation shows that for any x e R2, 1' p(s, x) ds T co as t T oc. Thus, for ...
متن کاملMultiple intersection exponents for planar Brownian motion
Let p ≥ 2, n1 ≤ · · · ≤ np be positive integers and B 1 , . . . , B n1 ; . . . ;B p 1 , . . . , B np be independent planar Brownian motions started uniformly on the boundary of the unit circle. We define a p-fold intersection exponent ςp(n1, . . . , np), as the exponential rate of decay of the probability that the packets ⋃ni j=1 B i j [0, t ], i = 1, . . . , p, have no joint intersection. The ...
متن کاملIntersection Exponents for Planar Brownian Motion
We derive properties concerning all intersection exponents for planar Brownian motion and we deene generalized exponents that loosely speaking correspond to non-integer numbers of Brownian paths. Some of these properties lead to general conjectures concerning the exact value of these exponents.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1996
ISSN: 0091-1798
DOI: 10.1214/aop/1042644710