A Comparative Study of non-Markovian Stochastic Processes in Marketing 公开

Pan, Jiening (2010)

Permanent URL: https://etd.library.emory.edu/concern/etds/sj1392567?locale=zh
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Abstract

Abstract
A Comparative Study of non-Markovian
Stochastic Processes in Marketing
By Jiening Pan
Non-Markovian(NM) stochastic processes exist widely in nature;
however, they have been largely ignored in traditional marketing
research. In this thesis, we investigate the consequences of such
NM behaviors both theoretically and experimentally. A stochastic
model analogous to the Ising model in statistical physics was used
to explain gaps between the Markovian and non-Markovian data
discovered in real surveys. Analytically a fixed point relation
between parameters is derived using the central limit theorem,
while detailed stochastic simulations are performed using a master
equation approach. Results from kinetic Monte Carlo (KMC)
simulations and analytical solutions coincide well with each other.
The model also has the potential to predict a larger group of
marketing outcomes if the model parameters are properly defined.

A Comparative Study of non-Markovian
Stochastic Processes in Marketing
By
Jiening Pan
B.S., Zhejiang University, 2008
Advisor:
Prof. Fereydoon Family, Ph.D
Prof. H.G.E. Hentschel, Ph.D
A thesis submitted to the Faculty of the
James T. Laney School of Graduate Studies of Emory University
in partial fulfillment of the requirements for the degree of
Master of Science
in Physics
2010

Table of Contents

Contents
List of Figures iv
Glossary v
1 Introduction 1
2 Experiment 5
2.1 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Real Experiment Data . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 Models 9
3.1 Model Settings, Basic Parameters and Terminology . . . . . . . . . 9
3.2 Ising Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2.1 Original Ising Model . . . . . . . . . . . . . . . . . . . . . . 10
3.2.2 From spin-spin coupling to the generalized Non-Markovian
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.3 Fermi Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4 Main Results from Modeling 16
4.1 Ising Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.1.1 Analytical Solution, Central Limit Approximating Approach 16
4.1.2 Analytical Solution, Master Equation Approach . . . . . . . 18
4.1.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . 19
4.1.3.1 Kinetic Monte-Carlo Simulation(KMC) . . . . . . . 20
4.1.3.2 Exact solution . . . . . . . . . . . . . . . . . . . . 24
4.2 Fermi Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.1 Simulation Results and Discussion . . . . . . . . . . . . . . . 31
5 Conclusions and Future Extensions 35
5.1 Parameter estimation, the methodology . . . . . . . . . . . . . . . . 35
5.2 Unification of Ising and Fermi model . . . . . . . . . . . . . . . . . 36
5.3 Correlation in Ising model . . . . . . . . . . . . . . . . . . . . . . . 37
A Survey Questionnaire 39
References 41

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