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Stochastic modelling, fall 2008


prof. Elja Arjas

Scope and fulfillment of course requirements

6 - 9 cu

The lecture course will be based on the monograph "Stochastic Modeling of Scientific Data" by Peter Guttorp, Chapman & Hall/CRC (1995).

The scope of the course is well described by the following except from its Preface: 

"Traditionally, applied probability texts contain a fair amount of probability theory, varying amounts of applications, and no data. Occasionally an author may touch upon how one would go about fitting a model to data, or use data to develop a model, but rarely is this topic given much weight. On the other hand, the few texts on statistical inference for stochastic processes mostly dwell at length upon the interesting twists that occur in statistical theory when data no longer can be assumed iid. But, again, they rarely contain any data. The intent of this text is to present some probability models, some statistics relevant to these models, and some data that illustrate some of the points that are made."

The lectures cover essential parts of the material in Chapters 2 (Discrete Markov chains) and 3 (Continuous time Markov chains), providing also a short introduction to Point processes discussed in Chapter 4.

The students following this course are strongly advised to have their own personal copy of this monograph. A preview of the book can be found at 

Active participation in the exercise sessions, and successful completion of the final exam, to be arranged in November, will earn you 6 cu. These credit points can be used as a substitute for the course 'Stokastiset prosessit' (6 cu) in the Applied Mathematics curriculum, to be lectured (in Finnish) in Spring 2009. Completing an additional project work, which is closely related to the course material, will earn you an additional 3 cu. The project work is optional, except for the students enrolled in the Master's Degree Programme in Bayesian Statistics and Decision Analysis, for whom the lecture course and the project work together correspond to the compulsory course 'Probability and stochastic processes' (9 cu).    


Advanced studies.


Period I (weeks 38 - 42) and Period II (weeks 44 - 45), Monday 10-12 and Thursday 12-14 in room B120. First lecture September 18.

Registration at the first lecture.

Exercise groups








12 - 14


Matti Pirinen

For the assignments and their solutions see

Final exam

The final exam of the course is on November 24, 2008, from 2 to 6 pm, in Exactum B119. Please register in advance.

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