Checking date: 01/04/2024

Course: 2024/2025

Stochastic Processes
Bachelor in Statistics and Business (Plan: 400 - Estudio: 203)

Coordinating teacher: JIMENEZ RECAREDO, RAUL JOSE

Department assigned to the subject: Statistics Department

Type: Compulsory
ECTS Credits: 6.0 ECTS


Requirements (Subjects that are assumed to be known)
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.
Skills and learning outcomes
Description of contents: programme
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.
Learning activities and methodology
Theory (4 ECTS). Lectures. Practice (2 ECTS). Problem solving lessons.
Assessment System
  • % end-of-term-examination 0
  • % of continuous assessment (assigments, laboratory, practicals...) 100

Calendar of Continuous assessment

Extraordinary call: regulations
Basic Bibliography
  • R. Durrett. Essentials of stochastic processes. Springer. 2012 (2nd ed.)
  • S.M. Ross. Stochastic Processes. John Wiley & Sons, inc.. 1996 (2nd. ed.)
Recursos electrónicosElectronic Resources *
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The course syllabus may change due academic events or other reasons.