Stochastic processes

  • Code: DT0052
  • Unit Coordinator: Alessia Nota
  • Programme: Double Degrees
  • ECTS Credits: 6
  • Semester: 2
  • Year: 1
  • Campus: University of L'Aquila
  • Language: English
  • Aims:

    Learning Outcomes

    At the end of the course, the students should:

    1. Developed the skills to model simple real problems and propose a solution;
    2. Solve theoretical problems, using the appropriate mathematical tools;
    3. Be able to read and understand other mathematical
    texts on related topics;
    4. Get a first flavour of the relevant research problems.

  • Content:

    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. Wiener processes and basic stochastic calculus: basic definitions and properties, Itô's formula, Stochastic Differential Equations.

  • Pre-requisites:

    Probability Theory and Analysis

  • Reading list:

    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 Srst look at Rigorous Probability Theory, J. Rosenthal, World Scientific.

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A network of 12 European Universities, coordinated by Department of Information Engineering, Computer Science and Mathematics (DISIM) at University of L'Aquila in Italy (UAQ)