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5. For the simple random walk, show that the probability po (2n) that the particle returns to the origin at the (2n)th step satisfies po (2n)~ (4pq)"/√√n, and use this to prove that the walk is persistent if and only if p = 1. You will need Stirling's formula: n! ~n" n²+½ e-√√2.

5. For the simple random walk, show that the probability po (2n) that the particle returns to the origin at the (2n)th step satisfies po (2n)~ (4pq)"/√√n, and use this to prove that the walk is persistent if and only if p = 1. You will need Stirling's formula: n! ~n" n²+½ e-√√2.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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5. For the simple random walk, show that the probability po (2n) that the particle returns to the origin at the (2n)th step satisfies po (2n)~ (4pq)"/√√n, and use this to prove that the walk is persistent if and only if p = 1. You will need Stirling's formula: n! ~n" n²+½ e-√√2.
Transcribed Image Text:5. For the simple random walk, show that the probability po (2n) that the particle returns to the origin at the (2n)th step satisfies po (2n)~ (4pq)"/√√n, and use this to prove that the walk is persistent if and only if p = 1. You will need Stirling's formula: n! ~n" n²+½ e-√√2.
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