Stochastic Processes and Simulation II
The course covers renewal theory, methods of stochastic simulation and the theory of Brownian motion.
Renewal Theory: A basic assumptions during previous courses is that stochastic processes are memoryless (Markovian). In the renewal theory we drop this assumption and study processes where the future advancement is not linked to the past. Therefore we lose some simplicity and elegance, but instead we obtain significantly more realistic results.
Brownian Motion: When a particle moves randomly, (like, for instance, a molecule in gas), its movement can often be viewed upon as a sum of a large number of impulses (collisions with other molecules in the gas). Due to the fact that the sums of stochastic variables are normally distributed, the particle's movements should approximately be normally distributed. Assuming that the time perspective of interest is a lot larger then the interval between two impulses, it follows that the particle's location is normally distributed. Then the particle describes Brownian motion. This mathematical model is frequently used, not only within physics, but also in many other areas of science and economy.
The course consists of two elements, theory and computer exercises.
Teaching Format
Instruction is given in the form of lectures, exercise sessions and computer exercises.
Assessment
Examination for the course is done with a written examination, and written presentation of the computer exercises.
Examiner
Ross: Introduction to probability models. Academic Press.
