Exercise 2.1.6 A random walk moves on the non-negative integers; when it is in state n, n > 0, it moves with probability Pn to n +1 and with probability 1– pn, to n– 1. When at 0, it moves to 1. Determine a network that gives this random walk and give a criterion in terms of the pn for recurrence of the random walk.

Exercise 2.1.6 A random walk moves on the non-negative integers; when it is in state n, n > 0, it moves with probability Pn to n +1 and with probability 1– pn, to n– 1. When at 0, it moves to 1. Determine a network that gives this random walk and give a criterion in terms of the pn for recurrence of the random walk.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 17EQ

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Exercise 2.1.6 A random walk moves on the non-negative integers;
when it is in state n, n > 0, it moves with probability Pn to n +1 and
with probability 1– pn, to n– 1. When at 0, it moves to 1. Determine
a network that gives this random walk and give a criterion in terms of
the pn for recurrence of the random walk.

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