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Markov Processes for Stochastic Modeling, 2nd Edition by Oliver Ibe

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8

Random Walk

8.1 Introduction

A random walk is derived from a sequence of Bernoulli trials. It is used in many fields including thermodynamics, biology, physics, chemistry, and economics where it is used to model fluctuations in the stock market.

Consider a Bernoulli trial in which the probability of success is p and the probability of failure is image. Assume that the experiment is performed every T time units, and let the random variable image denote the outcome of the kth trial. Furthermore, assume that the probability mass function (PMF) of is as follows: ...

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