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Course: 2021/2022

Stochastic Processes

(13716)

Bachelor in Statistics and Business (2008 Study Plan) (Plan: 146 - Estudio: 203)

Coordinating teacher: JIMENEZ RECAREDO, RAUL JOSE

Department assigned to the subject: Statistics Department

Type: Compulsory

ECTS Credits: 6.0 ECTS

Course: 3º

Semester: 2º

Requirements (Subjects that are assumed to be known)

Elementary Statistical Theory I Elementary Statistical Theory II

Objectives

SPECIFIC SKILLS. 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. CUTTING SKILLS: 1. Capacity for analysis and synthesis. 2. Problem solving. 3. Critical Thinking.

Skills and learning outcomes

Link to document

Description of contents: programme

1 - Introduction 1.1 - Random Variables 1.2 - Random Vectors 1.3 - Conditioned Expectation 1.4 - Stochastic processes 2 - Markov chains in discrete time 2.1 Definition 2.2 State classification 2.3 Stopping times 2.4 Limit Theorems 2.5 Limit and stationary distributions 3 - Martingales in discrete time 3.1 Definition 3.2 Optional Stopping Theorem 3.3 Wald's Equation 3.4 Gambler's ruin problem 4 - Continuous-time Stochastic Processes 4.1 Motivation 4.2 Various examples of processes with discrete state spaces. 4.3 Various examples of processes with continuous state spaces. 4.4 Applications

Learning activities and methodology

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

Assessment System

Final examination 40%. The remaining 60% will be grade through continuous evaluation, which will consist of tests, assignments and projects. All tests can contain application exercises, theoretical questions, and questions on computational practices. The student obtains a good grade in the continuous assessment may exempt the final exam.

% end-of-term-examination 40
% of continuous assessment (assigments, laboratory, practicals...) 60

Calendar of Continuous assessment

Basic Bibliography

R. Durrett. Essentials of stochastic processes. Springer. 2012 (2nd ed.)
S.M. Ross. Stochastic Processes. John Wiley & Sons, inc.. 1996 (2nd. ed.)

Electronic Resources *

R. Durrett · Essentials of Stochastic Processes : http://www.math.duke.edu/~rtd/EOSP/EOSP2E.pdf

(*) Access to some electronic resources may be restricted to members of the university community and require validation through Campus Global. If you try to connect from outside of the University you will need to set up a VPN

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