OBJECTIVES:
The aim is to provide theoretical knowledges of Stochastic Processes together with the know-how for modeling and solving actual problems by stochastic techniques.
PROGRAMME:
TIME AND LOCATION:
18 lessons in total
Every Tuesday and Thursday starting on February 15th and ending on Marzo 31st
| Day | Room | Time |
|---|---|---|
| Tuesdays | 4.1.01 (Getafe) | 09:30-11:30 |
| Thursdays | 4.1.02 (Getafe) | 12:00-14:00 |
FINAL EXAM: 
| Day | Room | Time |
|---|---|---|
| May 4th, 2011 | 7.3.J08 (Leganés) | 15:30-19:00 |
LECTURER:
Bernardo D'Auria
Room: 7.3.J29 (Juan Benet, Leganés)
email: 
ASSESSMENT CRITERIA:
Continuous Evaluation by mean of 3 homeworks (theoretical and/or applied) and one Final Exam to be done at the end of the course. The final mark of the course will be equal to 60% of the Continuos Evaluation mark plus 40% of the Final Exam mark.
REQUIREMENT:
Background in Mathematics, Probability and Statistics at Science/Technical graduate level.
PRACTICAL SESSIONS:
Three sets of theorical/practical/simulations exercices will be proposed.
BASIC BIBLIOGRAPHY:
- Durrett, R. (2001): Essentials of stochastic processes. Springer
- Durrett, R. (1996): Stochastic calculus : a practical introduction. CRC Press
- Ross, S.M. (2007): Introduction to probability models. Academic Press
- Ross, S.M. (1996): Stochastic processes. John Wiley & Sons
- Steele, J.M. (2000): Stochastic Calculus and Financial Applications. Springer.
ADDITIONAL BIBLIOGRAPHY:
- Brémaud, P.: Markov chains: gibbs fields, Monte Carlo simulation and queues. Springer-Verlag
- Feller, W.: An introduction to probability theory and its applications (vol. I & II). John Wiley & Sons
- Harrison, J.M.: Brownian motion and stochastic flow systems. R. E. Krieger
- Mikosch, T.: Elementary stochastic calculus :with finance in view. World Scientific
TIME AND LOCATION:
| Day | Room | Time |
|---|---|---|
| Tuesdays | 4.1.01 (Getafe) | 09:30-11:30 |
| Thursdays | 4.1.02 (Getafe) | 12:00-14:00 |
FINAL EXAM:
| Day | Room | Time |
|---|---|---|
| May 4th, 2011 | 7.3.J08 (Leganés) | 15:30-19:00 |
LECTURER:
Bernardo D'Auria
Room: 7.3.J29 (Juan Benet, Leganés)
email:
CHRONOGRAM:
| # | Day | Content | Notes | Prob. Set | Deadline Prob. Sets |
|---|---|---|---|---|---|
| February 2011 | |||||
| 01 | Tu - 15 | Introduction and basic notions. [R2] (§1.1, §1.2, §1.3 and §1.4) | |||
| 02 | Th - 17 | Introduction and basic notions. [R2] (§1.5 and §1.9) | |||
| 03 | Tu - 22 | The Poisson Process. [R2] (§2.1, §2.2 and §2.3) | |||
| 04 | Th - 24 | Renewal Theory. [R2] (§3.1, §3.2 and §3.3) | Comments | ||
| March 2011 | |||||
| 05 | Tu - 01 | Renewal Theory. [R2] (§3.3.1 and §3.3.2) Exercises. | Notes | #1 | |
| 06 | Th - 03 | Renewal Theory. [R2] (§3.4 and §3.4.1) | |||
| 07 | Tu - 08 | Renewal Theory. [R2] (§3.5 and §3.6) | |||
| 08 | Th - 10 | Markov Chains. [R2] (§4.1 and §4.2) | #1 | ||
| 09 | Tu - 15 | Markov Chains. [R2] (§4.2 and §4.3) | |||
| 10 | Th - 17 | Markov Chains. [R2] (§4.3) | #2 | ||
| 11 | Tu - 22 | Markov Chains. [R2] (§4.4) Semi-Markov Processes. [R2] (§4.8) | |||
| 12 | Th - 24 | Continuous-Time Markov Chains. [R2] (§5.1, §5.2 and §5.3) | #2 | ||
| 13 | Tu - 29 | Continuous-Time Markov Chains. [R2] (§5.4, §5.4.1 and §5.5) | |||
| 14 | Th - 31 | Brownian Motion. [R2] (§8.1, §8.2 and §8.3) | |||
| April 2011 | |||||
| 15 | Tu - 05 | Brownian Motion with drift. [R2] (§8.4 and §8.5) | |||
| 16 | Th - 07 | Brownian Motion with drift. [R2] (§8.4) Stochastic Calculus. [S1] (§6.4) | #3 | ||
| 17 | Tu - 12 | Stochastic Calculus. [S1] (§7.2, §8.0, §8.4-8.6, §9.0-9.3) | |||
| 18 | Th - 14 | Stochastic Calculus. [S1] (§10.0-10.3, §11.4) | #3 | ||
BASIC BIBLIOGRAPHY:
[D1] Durrett, R. (2001): Essentials of stochastic processes. Springer
[D2] Durrett, R. (1996): Stochastic calculus : a practical introduction. CRC Press
[R1] Ross, S.M. (2007): Introduction to probability models. Academic Press
[R2] Ross, S.M. (1996): Stochastic processes. John Wiley & Sons
[S1] Steele, J.M. (2000): Stochastic Calculus and Financial Applications. Springer.
