Checking date: 07/07/2020

Course: 2020/2021

Stochastic Processes
Study: Bachelor in Applied Mathematics and Computing (362)

Coordinating teacher: JIMENEZ RECAREDO, RAUL JOSE

Department assigned to the subject: Department of Statistics

Type: Compulsory
ECTS Credits: 6.0 ECTS


Competences and skills that will be acquired and learning results. SPECIFIC SKILLS Students will acquire knowledge and skills necessary to: 1. Knowing the theoretical foundations and the basic properties of stochastic processes 2. Stochastic Modelling of real cases. 3. Resolution of problems of Stochastic Nature. GENERAL SKILLS Students will be able to: 1. Develop their ability to think analytically 1. Become familiar with a statistical software 2. Establish a framework to solve problems 3. Develop their interactive skills 4. Enhance their critical thinking 5. Improve their learning skills and communication
Description of contents: programme
1. Introduction to Stochastic Processes. 1.1. Basic Definitions and Notations. 1.2. Examples: branching processes and queues. 1.3. Review of Conditional Expectation. 1.4. Review of Characteristic Functions and applications. 2. Discrete time Markov Chains. 2.1. Basic Definitions and Notations. 2.2 Chapman-Kolmogorov Equations and classification of states. 2.3. Asymptotic results. 2.4. First Step Analysis. 2.5. Random Walks and Success Runs. 2.6 The Geo/Geo/1 queue. 3. Renewal Theory and Poisson process. 3.1 Definition and basic notions. 3.2 The Elementary Renewal Theorem.¿ 3.3 The Key Renewal Theorem. 3.4 The Delayed Renewal Theorem. 3.5 Compound Poisson Process. 4. Continuous time Markov Chains. 4.1 Definition and basic notions¿ 4.2 Chapman-Kolmogorov Equations and Limit Theorems 4.3 Birth and Death Processes (M/M/m queues). 5. Continuous time Markov Processes: Brownian Motion. 5.1 Brownian Motion and Gaussian Processes. 5.2 Variations and Extensions. 5.3 Hitting times.¿ 5.4 Relation with Martingales.
Learning activities and methodology
- Clases magistrales: Presentación de conceptos, desarrollo de la teoría y ejemplos, 2.2 ECTS - Clases de resolución de problemas: 2.2 ECTS - Prácticas de ordenador: 0.6 ECTS - Sesiones de evaluación (exámenes de evaluación continua y examen final): 1 ECTS
Assessment System
  • % end-of-term-examination 40
  • % of continuous assessment (assigments, laboratory, practicals...) 60
Basic Bibliography
  • 1. Moshe Haviv. . A Course in Queueing Theory. . Springer. 2013
  • Sheldon M. Ross. . Stochastic Processes. . Wiley. 1995

The course syllabus and the academic weekly planning may change due academic events or other reasons.