Stochastic processes

Additional Info

  • ECTS credits: 6
  • Semester: 2
  • University: University of L'Aquila
  • Prerequisites:

     

    Probability theory and Real Analysis

  • Objectives:

     

    Students should:
    1. Develop the skills to model simple real problems and propose a solution;
    2. Solve theoretical problems, using the appropriate mathematical tools;
    3. Read the related texts and gain access to more advanced courses;
    4. Get a first flavour of the relevant research problems.

  • Topics:

     

    1. Discrete time processes: Markov chains in finite and countable space, limiting distribution;
    2. Continuous time processes: density and distribution of into-event time for Poisson process, applications and extensions: e.g. birth-and-death processes, queues, epidemics;
    3. Renewal processes: ordinary renewal process, renewal theorem, equilibrium
    renewal process, application to queues;
    4. Wiener processes and basic stochastic calculus: basic definitions and properties, It\^o's formula, Stochastic Differential Equations.

  • Books:

     

    1. Markov Chains, J.R. Norris, Cambridge University Press;
    2. Introduction to Stochastic Processes, G. Lawler, Chapman & Hall;
    3. Basic Stochastic Processes, A Course Through Exercises, Z. Brzezniak and T. Zastawniak, Springer;
    4. Probability and Random Processes, G. Grimmett and D. Stirzaker, 3rd Edition, Oxford University Press;
    5. A first look at Rigorous Probability Theory, J. Rosenthal, World Scientific.

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