Geometric Properties of 2-dimensional Brownian Paths
نویسندگان
چکیده
Let A be the set of all points of the plane C, visited by 2-dimensional Brownian motion before time 1. With probability 1, all points of A are “twist points” except a set of harmonic measure zero. “Twist points” may be continuously approached in C \ A only along a special spiral. Although negligible in the sense of harmonic measure, various classes of “cone points” are dense in A, with probability 1. “Cone points” may be approached in C \A within suitable wedges.
منابع مشابه
Geometric and Fractal Properties of Brownian Motion and Random Walk Paths in Two and Three Dimensions
There is a close relationship between critical exponents for proa-bilities of events and fractal properties of paths of Brownian motion and random walk in two and three dimensions. Cone points, cut points, frontier points, and pioneer points for Brownian motion are examples of sets whose Hausdorr dimension can be given in terms of corresponding exponents. In the latter three cases, the exponent...
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 کاملOutperformance Testing of a Dynamic Assets Portfolio Selection Supplemented with a Continuous Paths Levy Process
This study aims at getting a better performance for optimal stock portfolios by modeling stocks prices dynamics through a continuous paths Levy process. To this end, the share prices are simulated using a multi-dimensional geometric Brownian motion model. Then, we use the results to form the optimal portfolio by maximizing the Sharpe ratio and comparing the findings with the outputs of the conv...
متن کاملThree dimensional numerical study on a trapezoidal microchannel heat sink with different inlet/outlet arrangements utilizing variable properties nanofluid
Nowadays, microchannels as closed circuits channels for fluid flow and heat removal are an integral part of the silicon-based electronic microsystems. Most of previous numerical studies on microchannel heat sinks (MCHS) have been performed for a two-dimensional domain using constant properties of the working fluid. In this study, laminar fluid flow and heat transfer of variable properties Al2O3...
متن کاملStochastic Calculus and Anticommuting Variables
A theory of integration for anticommuting paths is described. This is combined with standard Itô calculus to give a geometric theory of Brownian paths on curved supermanifolds. This lecture concerns a generalisation of Brownian motion and Itô calculus to include paths in spaces of anticommuting variables. The motivation for this work comes originally from physics, where anticommuting variables ...
متن کامل