Checking date: 19/05/2022

Course: 2022/2023

Stochastic Processes
Study: Master in Statistics for Data Science (345)

Coordinating teacher: MEILAN VILA, ANDREA

Department assigned to the subject: Statistics Department

Type: Compulsory
ECTS Credits: 3.0 ECTS


Requirements (Subjects that are assumed to be known)
Probability, Programming in R
To acquire basic rudiments of the theory of stochastic processes. Modeling real problems through Markov and Poisson processes. To solve problems using the appropriate stochastic methodologies and techniques.
Skills and learning outcomes
Description of contents: programme
1. Introduction to stochastic processes 1.1. Definition and basic concepts. 1.2. Types of processes. 2. Discrete-time Markov chains. 2.1. Definition and basic computations. 2.2. Classification of states. 2.3. Limiting and stationary distributions. 2.4. Limit theorems. 2.5. ML estimation of transition probabilities. 3. Markov chain Monte Carlo. 3.1. The Metropolis-Hastings algorithm. 3.2. The Gibbs sampler. 3.3. MCMC diagnosis. 4. Poisson processes. 4.1. Introduction. 4.2. The Poisson process. 4.2.1. Inter-arrival times. 4.2.2. Infinitesimal probabilities. 4.2.3. The connection with the uniform distribution. 4.2.4. Thinning and superposition 4.3. Non-homogeneous Poisson processes. 5. Continuous-time Markov chains 5.1. Introduction 5.2. Transition function and transition rates 5.3. Long-term behaviour 5.4. Time-reversibility 6. Brownian motion and Gaussian processes 6.1. Brownian Motion 6.2. Transformations and Properties 6.3. Extensions of the Brownian Motion 6.4. Gaussian processes
Learning activities and methodology
In each class, theoretical concepts are introduced. Numerical and simulated exercises are shown for better understanding. Applications are also made with real data.
Assessment System
  • % end-of-term-examination 50
  • % of continuous assessment (assigments, laboratory, practicals...) 50
Calendar of Continuous assessment
Basic Bibliography
  • 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.

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