臺灣博碩士論文加值系統

對於用來分析隨機漫步的性質，局部中央極限定理是非常重要的定理。在很多書上都有對它做一些討論，但是他們討論的問題大都是在 d 維度整數晶格上簡單的隨機漫步。在這篇論文中我們將衍生的是在 d 維度三角晶格上隨機漫步的局步中央極限定理，當維度 d 等於2,3... .

Local Central Limit Theorem is a very important theorem for
analyzing the properties of random walks. There are discussions
in a lot of books, etc.. But most discussions are about
the theorem that the walk is simple random walk on Zd lattices.
In this thesis, we develop the Local Central Limit theorem of
random walks on d-dimensional triangular lattices for d=2, 3,... .

Contents
1 Introduction 1
2 Definitions and Notations 2
3 Fundamental Properties on Characteristic Function 5
4 Proof of Main Theorem 12

[1] Rick Durrett (2005), Probability: Theory and Examples, Third Edition, Bolinda Krohner.
[2] Robert B. Ash (2000), Probability and Measure Theory, Second Edition, Academic press.
[3] K. L. Chang (1974), A course in Probability Theory, Second Edition, academic. Press, New York.
[4] Gregory F. Lawler (1996), Intersections of random walks, Birkhauser Boston.
[5] Bernt Øksendal (1995), Stochastic Differential Equations.
[6] F. Harary (1969), Graph Theory, Addison-Wesley, New York.
[7] Peter G. Doyle and J. Laurie Snell (2000), Random walk and electric networks.
[8] Frank Spitzer (1964), Principles of Random Walk.
[9] B. Bollobas, F.Kirwan, P. Sarnak, C.T.C. Wall (2000), Random Walks on Infinite Graphs and Groups.