Event
STAT Colloquium: Shelemyahu Zacks, "Telegraph Process with Elastic Boundary"
Wednesday, January 25, 2017
3:15 p.m.
3206 Kirwan Hall (formerly the Mathematics Building)
Benjamin Kedem
bnk@umd.edu
Mathematics Department STAT Colloquium
Telegraph process with elastic boundary
Shelemyahu Zacks
Distinguished Professor Emeritus
SUNY Binghamton
Abstract
A particle moves on the real line starting at the origin. It moves up for a random length of time at velocity V(t)=1. At that point it moves down at velocity V(t)=-1, for a random time. This alternately renewal process is a basic Telegraph process. The first time the particle returns to the origin it is absorbed with probability p or reflected up with probability 1-p. If the particle is reflected a new renewal cycle starts. We develop the distribution of cycle length and its moment. The distribution of the time till absorption and its moments.
