2007/2008MSG800 (GU), MVE170 (EM) Basic Stochastic Processes, 7.5 credit pointsMSG860 (F) Basic Stochastic Processes, TMS125 Stochastic Processes, 4.5 credit pointsThis is a first course in stochastic models for senior undergraduate students in engineering, mathematical statistics, and applied mathematics. The students are assumed to be familiar with the elementary theory of probability.The theoretical part of the course provides a solid framework in which a variety of applications will be considered. Course Content The Poisson process and related topics The Poisson process The memoryless property Merging and splitting of Poisson processes The M|G|infinity queue The Poisson process and the uniform distribution Renewal-reward processes The renewal process. The renewal function and the excess variable The renewal-reward process. Limit theorems. Examples on application The formula of Little Poisson arrivals see time averages Discrete-time Markov chains The model. Examples Transient analysis The equilibrium probabilities Computation of the equilibrium probabilities Continuous-time Markov chains The model. Examples The balance equations. Interpretation of the equilibrium probabilities. The flow rate equation method Continuous-time Markov chains with rewards Computation of the equilibrium probabilities: Kolmogoroff's forward differential equations Markov chains and queues The Erlang delay model: the M/M/1 queue. Course Book A First Course in Stochastic Models by Henk C. Tijms. Organization The course is run on two levels, worth 7.5 and 4.5 credit points respectively. It comprises lectures, classes with exercises and discussions, two take home problem-solving examinations, and a written examination in the theory. |
MSG800 (GU), MVE170 (EM) Basic Stochastic Processes, 7,5 credit pointsMSG860 (F) Basic Stochastic Processes, TMS125 Stochastic Processes, 4.5 credit points
Lecturers and exercises Course material. Examination and evaluation of the course
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