基本素養 Basic Literacy

科技人文素養
Technological and Cultural literacy
環境與社會關懷
Environmental and Social Care
溝通合作能力與國際宏觀視野
Ability to communicate effectively with others and work in a team with developed international perspective.

核心能力 Competence

專業與跨域能力
Professional and interdisciplinary capacity
創新思考及定義、獨立解決問題之能力
Innovative thinking as well as the ability to define and solve problems independently
語文與溝通能力,進而協調跨領域人員整合
Language and communication skills to coordinate the integration of interdisciplinary personnel
設計、驗證及與產業實作整合之能力,攜手促進產業轉型升級
The ability to design, verify, and integrate with industrial implementations, and work together to promote industrial transformation and upgrading
自我學習成長之能力:國際視野、基本素養
Developed sense of self- improvement: International Perspective, Principle Literacy

課程概述 Course Description

本課程將介紹隨機過程的基本理論,該理論提供了許多自然科學,工程學以及社會科學中的建模方法。隨機過程是受隨機現象影響的時變系統之數學建模。我們使用各種機率技術以數學上合理的方式來描述隨機量。 本課程從對基本機率概念的回顧開始,著重於離散和連續時間馬爾可夫鍊的理論。本課程也涵蓋了一些最重要的隨機過程(泊松,高斯,排隊模型)。 在應用上,我們將著重於計算機科學中出現的隨機建模,尤其是在隨機轉換系統上。這些應用解釋如何透過並行與通信系統將計算整合至網宇實體系統中。
This course introduces a basic theory of stochastic process, which provides a large number of modelling in natural sciences and engineering as well as in social sciences. Stochastic process is a mathematical modeling of time-dependent systems subject to random phenomena. Various probability techniques capture the random quantities in a mathematically sound way. Starting with a review of basic probability concepts, this course focuses on the theory of discrete and continuous Markov processes. The course also covers some most important types of stochastic processes (Poisson, Gaussian, queuing models). Real world application of the theory is emphasized on stochastic modelling arising in computer science, especially on stochastic transition systems. The application explains how to integrate computation into cyber physical systems in terms of concurrent and communicating systems.

課程學習目標 Course Objectives

  • Markov Process
  • Poisson Process and Application to Queueing Model
  • Stochastic Modelling in Computer Science
  • 課程進度 Progress Description

    進度說明 Progress Description
    1I. Probability Review (random variables and their characteristics, various distributions, independence and sums, etc)
    2II. Markov Chains (discrete time) II-i State Spaces and Transition Matrices
    3II-ii Classification of States
    4II-iii Chapman Kolmogorov Equation
    5II-iv Stationary Distributions: Detailed Balance and Reversibility
    6II-v Algorithm to Check Reversibility
    7II-vi Limit Behavior (Convergence to Equilibrium)
    8II-vii Ergodic Theorem
    9III. Stochastic Modelling in Computer Science I (stochastic automata)
    10IV. Poisson Processes IV-i Continuous Time Stochastic Processes, Exponential Distributions
    11IV-ii Limit Theorem (the Law of Rare Events)
    12 V. Markov Processes (continuous time) V-i Transition Rate Matrices and Their Exponentials
    13V-ii Kolmogorov Forward and Backward Equations
    14V-iii Time Reversal
    15VI. Stochastic Modelling in Computer Science II (stochastic petri nets)
    16VII. Queueing Systems
    17VIII. Brownian Motion and Gaussian Processes
    18IX. OPTIONAL Markov Decision Process Simulation Algorithm (Markov Chain Monte Carlo)
     以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

    課程是否與永續發展目標相關調查
    Survey of the conntent relevant to SDGs

    本課程與SDGs相關項目如下:
    This course is relevant to these items of SDGs as following:
    • 就業與經濟成長 (Decent work and Economic growth)
    • 工業、創新與基礎建設 (Industry Innovation and infrastructure)

    有關課程其他調查 Other Surveys of Courses

    1.本課程是否規劃業界教師參與教學或演講? 否
    Is there any industry specialist invited in this course? How many times? No
    2.本課程是否規劃含校外實習(並非參訪)? 否
    Are there any internships involved in the course? How many hours? No
    3.本課程是否可歸認為學術倫理課程? 否
    Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics? No
    4.本課程是否屬進入社區實踐課程? 否
    Is this course recognized as a Community engagement and Service learning course? Which community will be engaged? No

    教師上傳大綱內容
    本資訊僅提供本校師生參考。有著作權,非本校人員若欲使用本資訊,請洽本校取得授權。
    © (2008-2022) National Cheng Kung University ALL RIGHTS RESERVED.

    濱野正浩-隨機過程.pdf