Course: 2019/2020

Stochastic Processes

(13716)

Students are expected to have completed

Elementary Statistical Theory I
Elementary Statistical Theory II

Competences and skills that will be acquired and learning results. Further information on this link

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.

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 - Markov Chains in continuous time
4.1 Definition
4.2 State classification
4.3 Stopping times
4.4 Limit Theorems
4.5 Limit and stationary distributions
4.6 Poisson Process
5 - Stochastic Processes in continuous time
5.1 Definition and examples
5.2 The Brownian motion
5.3 Gaussian processes

Learning activities and methodology

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

Assessment System

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

Basic Bibliography

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

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

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**More information: **http://www.est.uc3m.es/esp/nueva%5Fdocencia/getafe/ciencias%5Festadisticas/procesos%5Festocasticos/