Hisashi Kobayashi's Blog

Sherman Fairchild University Professor Emeritus of Electrical Engineering and Computer Science, Princeton University

CUP Book Interview


Hi. Thank you for visiting this YouTube video.

I am Hisashi Kobayashi, a professor at Princeton University and the first author of Probability, Random Processes and Statistical Analysis, published by Cambridge University Press.

This video is taken at NICT, the National Institute of Information and Communications Technology, in Tokyo, Japan, where I participate in their research on a future Internet architecture project called the New Generation Network.

I suppose that you have visited the website of the book before you clicked this video and I hope that by looking at the table of contents shown at the website, you already have a pretty good idea about the book.

The book is an outgrowth of the lectures I gave at Princeton over the past ten years to graduate students in the Electrical Engineering Department, but the scope of the book is much broader than my lecture notes. My coauthors and I believe that students and researchers in such fields as econometrics, machine learning, mathematical finance, operations research and bioinformatics will find this book useful.

When I came to Princeton as a Ph.D. student in 1965, I attended the lectures given by the late Professor William Feller in the Statistics Department. He is the author of classic volumes, Probability Theory and Its Applications, Volumes I and II, published more than 50 years ago. I still use Professor Feller:s volumes quite frequently since the fundamentals and theory have not changed very much, and his treatment of the subjects is comprehensive. So my desire is that students and researchers fifty years from now, long after I will have passed on, will find our book still valuable.

Here are the main features of our book.

  1. In the introductory chapter, we provide not only an overview of and motivations for the subject matters, but also an historical note on how some of the important developments in probability theory, random processes and statistical analysis have taken place. I hope that you will find the historical notes as fascinating as I do.
  2. Probability theory and statistical analysis are intimately related to each other, yet very few textbooks treat them in as cohesive a manner as our book does.
  3. There are two schools of thought in statistical models. One is the so-called frequentist approach and the other is Bayesian approach. The latter is becoming increasingly important in econometric models and machine learning. The recent popularity of the Markov chain Monte Carlo method is one such example. Hidden Markov models and model parameter estimation using the Expectation-Maximization algorithm is another example. Hidden Markov models and the EM algorithm are increasingly important in signal processing theory and its applications as well.
  4. Some of our engineering students often find employment in financial sectors. Our book provides a comprehensive treatment of such topics as random walk, Brownian motion, geometric Brownian motion and Ito processes, and derives the famous Black Scholes differential equation for option trading. Thus, this book serves as a good introduction to mathematical finance.
  5. Queueing theory is a branch of applied probability theory, and finds its applications in logistics, and in traffic theory for communication networks, Although books on queueing models abound, few books provide a comprehensive treatment on loss models such as the generalized Erlang and Engset loss models.
  6. The solutions to all Exercise problems can be accessed by those who register as instructors at the website of Cambridge University Press. Lecture slides will be also made available. The supplementary materials on prerequisite topics such as matrix theory, Dirac:s delta function, contour integration, etc., will be available online.

So I do hope that you will find the book useful as a textbook for classroom teaching and/or as a reference book in your research and study. Thank you for your attention.

今日は。 この ユー・チューブ ビデオをご覧下さり有難うございます。

私はプリンストン大学教授の小林久志と申します。この度、ケンブリッジ出版から発行された Probability, Random Processes and Statistical Analysis の著者の一人であります。


この本の前半は、過去10年程、プリンストン大学の電気工学科で、大学院生を相手に私が講義して参った講義録をベースにしたものですがこの本のスコープはもっと幅の広いものであります。 計量経済学、機械学習、数理ファイナンス、オペレーションズ・リサーチ、生物情報学等の分野の学生、研究者の皆様にもお役に立てるものと、私共著者は信じております。

名著、確率論とその応用、Vol. I and Vol. II, はいまだに私の座右の書としてしばしば使っています。私の願いはこれから50年後、私があの世に経った後も、私達の本が学生や研究者の皆さんに読まれ使って頂ければという事であります。


  1. 第一章では、本全体の展望と動機づけを論ずるだけでなく、確率論、ランダム過程、及び統計解析における重要なる発展が如何に起こったか、その歴史的記述も提供しています。読者の皆様にもご興味をもっていただけると思います。
  2. 確率論と統計解析は、互いに密な関係にあります。それにも拘わらず双方を密着して取り扱っている教科書は他に余りありません。
  3. 統計的モデルには二つの流派があります。 頻度数に基づくfrequentist 派–度論者—とBayes定理に基づくBayesian派であります。後者は最近,計量経済学や機械学習では益々重要になっています。マルコフ連鎖モンテカルロの普及がその一例です。隠れマルコフ・モデルにおいてExpectation-Maximization アルゴリズムに基づいてモデル・パラメターを評価するのも、その例です。隠れマルコフ・モデルやEMアルゴリズムは信号処理理論やその応用分野で益々重要になってきています。
  4. 工学系の学生の中にも、金融関係分野に就職する者がいます。この本はランダムウォーク、ブラウン運動、幾何学的ブラウン運動,Ito プロセスなどを徹底的に論じ、オプション取引の為のかの有名なブラック・ショールズ偏微分方程式を導出します。従ってこの本は数理ファイナンスへの入門書として役立つと思います。
  5. 待ち行列理論は応用確率論の一分野であり、物流や通信ネットワークにおけるトラフィック理論などに応用されます。待ち行列理論に関する本は多数ありますが、一般化されたアーラングやエングセットの損失モデル等を論じている教科書は殆ど皆無と思います。
  6. インストラクターとしてケンブリッジ出版のウェブサイトに登録された方々は演習問題の解答集にアクセス出来ます。インストラクター用のスライドも近々完成の予定です。行列式理論、デイラックのデルタ関数、周回積分などの予備知識を論じた補助教材もオンラインで提供致します。


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