2 7 Ju n 20 01 Statistics of the occupation time for a random walk in the presence of a moving boundary
نویسندگان
چکیده
We investigate the distribution of the time spent by a random walker to the right of a boundary moving with constant velocity v. For the continuous-time problem (Brownian motion), we provide a simple alternative proof of Newman's recent result [J. Phys. A 34, L89 (2001)] using a method due to Kac. We then discuss the same problem for the case of a random walk in discrete time with an arbitrary distribution of steps, taking advantage of the general set of results due to Sparre Andersen. For the binomial random walk we analyse the corrections to the continuum limit on the example of the mean occupation time. The case of Cauchy-distributed steps is also studied.
منابع مشابه
A Random Walk with Exponential Travel Times
Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...
متن کاملAsymptotic Approximations of the Solution for a Traveling String under Boundary Damping
Transversal vibrations of an axially moving string under boundary damping are investigated. Mathematically, it represents a homogenous linear partial differential equation subject to nonhomogeneous boundary conditions. The string is moving with a relatively (low) constant speed, which is considered to be positive. The string is kept fixed at the first end, while the other end is tied with the ...
متن کاملA Fuzzy Random Walk Technique to Forecasting Volatility of Iran Stock Exchange Index
Study of volatility has been considered by the academics and decision makers dur-ing two last decades. First since the volatility has been a risk criterion it has been used by many decision makers and activists in capital market. Over the years it has been of more importance because of the effect of volatility on economy and capital markets stability for stocks, bonds, and foreign exchange mark...
متن کاملA PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...
متن کاملCentral Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
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 2001