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| MATH1222-1 | Introduction to stochastic processes
- Markov chains
- Markov process
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| Duration : | Markov chains : 20h Th, 10h Pr
Markov process : 10h Th, 20h Mon. WS
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| Number of credits : |
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| Lecturer : | Markov chains : Pierre Geurts, Yvik Swan
Markov process : Yvik Swan
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| Coordinator : | Yvik Swan |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the second semester |
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Course contents :
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 | | Markov chains |
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| Markov chains in discrete time (definition, classification of states, absorption time, strong Markov property, recurrence and transience, invariant distributions, convergence to equilibrium). Markov chains in continuous time (Q-matrices and exponential, Poisson process, life and death processes, properties of Markov chains in continuous time, classification of states, recurrence and transience, invariant distribution, convergence to equilibrium ). Queues (Kendall notation, occupancy rates, performance metrics, file M / M / m). Other applications (Markov Chain Monte Carlo, Hidden Markov Models)
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| | Markov process |
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| Sequel of preceding course : we study the main Markovian processes (in particular Brownian motion).
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Learning outcomes of the course :
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| | Markov chains |
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| After the course, students will master the main properties of most classical stochastic processes. |
| | Markov process |
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| After the course, students will master the main properties of most classical stochastic processes. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| | Markov chains |
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| Basic probability theory. Elementary notions of calculus and linear algebra. Understanding of R and/or Matlab. |
| | Markov process |
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| Basic probability theory. Elementary notions of calculus and linear algebra. Understanding of R and/or Matlab. |
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Planned learning activities and teaching methods :
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| | Markov chains |
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| In addition to the traditional classroom course, the course includes 10 hours traditional exercise sessions (10h Pr, ex cathedra).
Students from Montefiore will also have 30 hours of personal research work (30h TD). This work will be carried out in groups, in ways yet to be determined (responsible : Prof. Pierre Geurts) |
| | Markov process |
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| In addition to the traditional classroom course, the course includes 10 hours traditional exercise sessions (10h Pr, ex cathedra).
Students from Montefiore will also have 30 hours of personal research work (30h TD). This work will be carried out in groups, in ways yet to be determined (responsible : Prof. Pierre Geurts) |
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Mode of delivery (face-to-face ; distance-learning) :
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Recommended or required readings :
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| | Markov chains |
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| Partial course notes (including exercise sets) will be made available through MyULg.
Bibliography
- Norris, James R. (1998). Markov chains. Cambridge University Press.
- Ross, Sheldon (2006). Introduction to probability models. Academic Press. |
| | Markov process |
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| Partial course notes (including exercise sets) will be made available through MyULg.
Bibliography
- Norris, James R. (1998). Markov chains. Cambridge University Press.
- Ross, Sheldon (2006). Introduction to probability models. Academic Press. |
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Assessment methods and criteria :
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| | Markov chains |
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| Montefiore students : the final grade will be a weighted average of two grades :
- that obtained after a written exam held in June (concerning both theory and exercises)
- the grade obtained after evaluation of a project
Students from the mathematics departement : see Partim 2 |
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| Students of the mathematics department : the final grade will be the result of an exam concerning both Partims of the Stochastic Processes course. |
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Work placement(s) :
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Organizational remarks :
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Contacts :
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| | Markov chains |
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| Yvik Swan
Université de Liège
Département de Mathématique,
Grande Traverse, 12, Sart Tilman,
B-4000 Liège
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| | Markov process |
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| Yvik Swan
Université de Liège
Département de Mathématique,
Grande Traverse, 12, Sart Tilman,
B-4000 Liège
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