Last zero time or maximum time of the winding number of Brownian motions
نویسنده
چکیده
In this paper we consider the winding number, θ(s), of planar Brownian motion and study asymptotic behavior of the process of the maximum time, the time when θ(s) attains the maximum in the interval 0 ≤ s ≤ t. We find the limit law of its logarithm with a suitable normalization factor and the upper growth rate of the maximum time process itself. We also show that the process of the last zero time of θ(s) in [0, t] has the same law as the maximum time process.
منابع مشابه
Long Time Asymptotics of Heat Kernels and Brownian Winding Numbers on Manifolds with Boundary
Let M be a compact Riemannian manifold with smooth boundary. We obtain the exact long time asymptotic behaviour of the heat kernel on abelian coverings ofM with mixed Dirichlet and Neumann boundary conditions. As an application, we study the long time behaviour of the abelianized winding of reflected Brownian motions in M . In particular, we prove a Gaussian type central limit theorem showing t...
متن کاملInvestigation of unbalanced magnetic force in permanent magnet brushless dc machines with diametrically asymmetric winding
The purpose of this paper is the calculation of Unbalanced Magnetic Force (UMF) in permanent magnet brushless DC (PMBLDC) machines with diametrically asymmetric winding and investigation of UMF variations in the presence of phase advance angle. This paper presents an analytical model of UMF in surface mounted PMBLDC machines that have a fractional ratio of slot number to pole number. This model...
متن کاملWinding Number of Fractional Brownian Motion
We find the exact winding number distribution of Riemann-Liouville fractional Brownian motion for large times in two dimensions using the propagator of a free particle. The distribution is similar to the Brownian motion case and it is of Cauchy type. In addition we find the winding number distribution of fractal time process, i.e., time fractional Fokker-Planck equation, in the presence of fini...
متن کاملEFFECT OF TIME-DEPENDENT TRANSPIRATION ON AXISYMMETRIC STAGNATION-POINT FLOW AND HEATTRANSFER OF A VISCOUS FLUID ON A MOVING CIRCULAR CYLINDER
Effect of time dependent normal transpiration on the problem of unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder moving simultaneously with time-depended angular and axial velocities and with time-dependent wall temperature or wall heat flux are investigated. The impinging free stream is steady with a strain rate . A re...
متن کاملProbability that the maximum of the reflected Brownian motion over a finite interval [0; t] is achieved by its last zero before t
We calculate the probability pc that the maximum of a reflected Brownian motion U is achieved on a complete excursion, i.e. pc := P ( U(t) = U∗(t) ) where U(t) (respectively U∗(t)) is the maximum of the process U over the time interval [0, t] (resp. [ 0, g(t) ] where g(t) is the last zero of U before t).
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 2014