Probability Linear Algebra R Programming

The course aims to develop the following competences: 1) Capacity to formulate basic stochastic process models (Poisson, Markov chains, Brownian motion) in diverse applications; 2) capacity to analyze such models based on an understanding of their fundamental properties; 3) capacity to investigate numerically such models using software.

1. The Poisson process. 1.1 Introduction and motivation; interarrival and waiting time distributions; conditional distribution of the arrival times. 1.2 Extensions and applications; nonhomogeneous Poisson process; compound Poisson process; conditional Poisson process. 2. Markov chains 2.1 Introduction and motivation; discrete-time chains; Chapman-Kolmogorov equations; examples; 2.2 Limiting distribution; stationary distributions; 2.3 Communicating classes; irreducible chains; classification of states; periodicity; ergodicity; limit theorems; applications. 3. Brownian motion 3.1 Introduction and motivation; hitting times, maximum variable and arc sine laws; variations on Brownian motion. 3.2 Brownian motion with drift; diffusion equations; applications.

Theoretical-practical classes with web-based supporting material. Computational sessions with the R software. The teaching methodology has an eminently practical approach, being based on the analysis and solution of stochastic process models arising in diverse application areas.