Course Contents This course introduces various stochastic processes and Monte Carlo simulation to model and analyze aerospace engineering
systems under uncertainty. The topics covered in the course are as follows:
1. Markov chains: Markov property, Chapman-Kolmogorov equations, ergodicity, transition probability matrix, Monte Carlo
simulation.
2. Discrete-Time Continuous-State stochastic processes: linear difference equations, Monte Carlo simulation.
3. Continuous-Time Markov chains: Q-matrix, stationarity, Monte Carlo simulation.
4. Poisson processes: properties, time discretization, Monte Carlo simulation.
5. Brownian motion: properties, Monte Carlo simulation.
6. Stochastic differential equations, Monte Carlo simulation.
The stochastic processes above are illustrated by means of applications in air transportation such as, for instance, aircraft
maintenance and airport operations under uncertainty.
Study Goals The aim of this course is to provide students with a working understanding of a variety of stochastic processes that are of
relevance in aerospace engineering. At the end of the course, the students should be able to:
1. State the defining properties of various stochastic processes.
2. Model various applications in air transportation using appropriate stochastic processes.
3. Evaluate the performace of various stochastic models in air transportation by conducting an analytical analysis or by means of
Monte Carlo simulation.
5. Explain the difference in results between the Monte Carlo simulation and the analytical results.
6. Identify the advantages and limitations of Monte Carlo simulation
