Stochastic Processes in Biomedicine

Teacher: dr. Hrvoje Šikić, professor
Associate: dr. Vanja Wagner, assistant professor
Semester: first or second
ECTS: 4
Elective course

To acquire basic knowledge of the most important types of stochastic processes, to learn their properties and to be introduced to some simple modelling techniques in stochastic environment.

After the completion of this course, students are expected to be able to:

  1. Recognize, analyse, and construct basic types of stochastic processes,
  2. Apply analysis techniques to study sample paths of various stochastic processes,
  3. Understand and apply in biomedical situations basic types of Markov processes, discrete and continuous,
  4. Understand and apply in biomedical situations basic types of martingales.
  1. Introduction. Conditional Expectations. Stochastic Processes, Discrete vs Continuous. Filtrations. Stopping Times. Sample Paths.
  2. Poisson Process. Random Walk. Markov Chains. Transition Matrix. Invariant Measures. Examples and Applications.
  3. Discrete Time Martingales. Optional Stopping Theorem. Limit Theorems. Examples and Applications.
  4. Brownian Motion. Levy Processes. Martingale Characterizations. Continuous and Cadlag Processes. Examples and Applications.
  5. General Markov Processes. Introduction to Semigroups. Feller Processes. Examples and Applications.
  • Course objectives

    To acquire basic knowledge of the most important types of stochastic processes, to learn their properties and to be introduced to some simple modelling techniques in stochastic environment.

  • Expected learning outcomes

    After the completion of this course, students are expected to be able to:

    1. Recognize, analyse, and construct basic types of stochastic processes,
    2. Apply analysis techniques to study sample paths of various stochastic processes,
    3. Understand and apply in biomedical situations basic types of Markov processes, discrete and continuous,
    4. Understand and apply in biomedical situations basic types of martingales.
  • Course content

    1. Introduction. Conditional Expectations. Stochastic Processes, Discrete vs Continuous. Filtrations. Stopping Times. Sample Paths.
    2. Poisson Process. Random Walk. Markov Chains. Transition Matrix. Invariant Measures. Examples and Applications.
    3. Discrete Time Martingales. Optional Stopping Theorem. Limit Theorems. Examples and Applications.
    4. Brownian Motion. Levy Processes. Martingale Characterizations. Continuous and Cadlag Processes. Examples and Applications.
    5. General Markov Processes. Introduction to Semigroups. Feller Processes. Examples and Applications.
PMF
EU fondovi
UNI-ZG