| Code |
15650
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| Year |
2
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(45H)
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| Scientific area |
Mathematics
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Entry requirements |
Does not have.
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Learning outcomes |
Formalize the theory of stochastic processes, with emphasis on the main classes of stochastic processes.
Apply the theory of Stochastic Processes in the modeling and resolution of problems related to random phenomena that evolve in time and that arise in the various areas of knowledge.
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Syllabus |
1. First concepts in stochastic processes: law of probability of a stochastic process; stationary stochastic processes in the strict sense and in the broad sense; independent increment processes, first examples of Gaussian processes and counting processes.
2. Poisson processes: axiomatic; homogeneity; compound processes; properties of the sequence of the times between arrivals and waiting times.
3. Markov chains: discrete time and continuous time; transition probabilities; Chapman-Kolmogorov equations;classification of states; asymptotic results; birth and death processes.
4. Queues: average arrival and service rates; traffic intensity; average customer numbers and average waiting times in models with Poissonian arrivals.
5. Linear processes: auto-regressive; moving averages; characteristics and time connections.
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Main Bibliography |
Karlin, S., Taylor, H.M. (1975) A First Course in Stochastic Processes, Academic Press.
Resnick, S. (1992) Adventures in Stochastic Processes, Birkhäuser, Boston.
Ross, S.M. (1995) Stochastic Processes, John Wiley & Sons, New York.
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Language |
Portuguese. Tutorial support is available in English.
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