Checking date: 05/05/2025 17:38:31


Course: 2025/2026

Stochastic Processes
(17754)
Master in Statistics for Data Science (Plan: 386 - Estudio: 345)
EPI


Coordinating teacher: NIÑO MORA, JOSE

Department assigned to the subject: Statistics Department

Type: Compulsory
ECTS Credits: 3.0 ECTS

Course:
Semester:




Requirements (Subjects that are assumed to be known)
Probability Linear Algebra R Programming
Objectives
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.
Learning Outcomes
Description of contents: programme
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.
Learning activities and methodology
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.
Assessment System
  • % end-of-term-examination/test 0
  • % of continuous assessment (assigments, laboratory, practicals...) 100

Calendar of Continuous assessment


Basic Bibliography
  • Blanco Castaneda, L., Arunachalam, V., Dharmaraja, S.. Introduction to probability and stochastic processes with applications. Wiley. 2012
  • Dobrow, R. P. . Introduction to stochastic processes with R. Wiley. 2016
  • Durrett, R.. Essentials of stochastic processes. Springer. 2012
  • S.M. Ross. Introduction to probability models. Academic Press. 2007
Additional Bibliography
  • Norris, J.R.. Markov Chains. Cambridge University Press. 1997
  • Ross, S.M.. Stochastic Processes. Wiley. 1996

The course syllabus may change due academic events or other reasons.