632-seppalainen-07spfin

632-seppalainen-07spfin - 632 Introduction to Stochastic...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 632 Introduction to Stochastic Processes Spring 2007 Final Exam Instructions: Show calculations and give concise justifications for full credit . Points add up to 200. 1. Born again branching process. Let { p k } k< be the offspring distribution of a branching process. Assume 0 < p < 1 so that interesting behavior is possible and let m be the mean of the offspring distribution. Let the process begin with one progenitor, and let X n be the population size of the n th generation with X = 1. The Galton-Watson branching process we studied in Chapter 1 was ab- sorbed at zero if it ever dies out. Now we give the process a chance to come to life again after extinction. Take another parameter 0 < < 1. Here is the transition rule for X n : (i) If X n > 0 the next state X n +1 is determined by the branching process transition with offspring distribution { p k } . (ii) If X n = 0 we put X n +1 = 1 with probability and put X n +1 = 0 with probability 1- ....
View Full Document

Page1 / 2

632-seppalainen-07spfin - 632 Introduction to Stochastic...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online