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Glossary
Semester (Sem)
1First Semester
2Second Semester
AAnnual course
Educational activities
BIdentifying activities
Language
Course completely offered in italian
Course completely offered in english
--Not available
Innovative teaching
The credits shown next to this symbol indicate the part of the course CFUs provided with Innovative teaching.
These CFUs include:
  • Subject taught jointly with companies or organizations
  • Blended Learning & Flipped Classroom
  • Massive Open Online Courses (MOOC)
  • Soft Skills
Degree ProgrammesCambia LinguaCambia Lingua
Course Details

Context
Academic Year 2014/2015
School School of Industrial and Information Engineering
Name (Master of Science degree)(ord. 270) - MI (403) Mathematical Engineering
Track MSC - Scienze computazionali per l'ingegneria
Programme Year 2

Course Details
ID Code 095966
Course Title STOCHASTIC DYNAMICAL MODELS
Course Type Mono-Disciplinary Course
Credits (CFU / ECTS) 8.0
Semester First Semester
Course Description Discrete time Markov chains. Structure of transition matrices, transient and recurrent states, Perron-Frobenius theorem, convergence towards invariant measures. Discrete time martingales, stopping theorem and applications to Markov chains, maximal inequality, Doob inequality, convergence theorems. Introduction to the general theory of continuous-time stochastic processes. Poisson process, independence of increments, exponential sojourn times. Renewal processes, law of large numbers and central limit theorem. Applications to reliability theory. Continuous time Markov chains, queues, transition rates, sojourn times. Forward and backward Kolmogorov equations. Invariant distributions and ergodic theorem. M/M/1 and M/M/k queues, stationary dynamics. Brownian motion, Ornstein-Uhlenbeck process and diffusion models (hints).
Scientific-Disciplinary Sector (SSD)
Educational activities SSD Code SSD Description CFU
B
MAT/06
PROBABILITY AND STATISTICS
8.0

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