Elementary Statistical Theory I Elementary Statistical Theory II

1. Knowing the theoretical foundations and the basic properties of stochastic processes. 2. Solve problems based on the studied stochastic models. 3. Simulating techniques for Markov Chains. 1. Capacity for analysis and synthesis. 2. Problem solving. 3. Critical Thinking.

1. Introduction 1.1 Basic concepts and classification of random processes. 1.2 Finite-dimensional distributions. Transition probabilities. Conditional expectation. 2 ¿ Discrete time processes 2.1 Examples of discrete-time processes. The simple random walk and the player's ruin. Martingales in discrete time. 2.2 Markov chains in discrete time. State classification. Stop times. limit theorems. Limit and stationary distributions. 3 - Continuous time processes 3.2 Examples of continuous-time processes with discrete state spaces. Renewal Processes. Queues and processes of birth and death. Poisson's process. Non-homogeneous Poisson process. Superposition of Poisson Processes. 3.3 Examples of processes with continuous state space. Processes with independent increments. The Brownian motion.

Theory (4 ECTS). Lectures. Practice (2 ECTS). Problem solving lessons.