MathMods :: Joint MSc

Additional Info

• ECTS credits: 6
• University: Autonomous University of Barcelona
• Semester: 3
• Lecturer 1: Vicenç MÉNDEZ
• Objectives:

   

  This is a course in basic stochastic processes. Many systems evolve over time with an inherent amount of randomness. The purpose of this course is to develope and analyse probability models that capture the features of the system under study to predict the short and long term effects that this randomness will have on the system under consideration.

• Topics:

   

  Bernoulli Processess, random walks; Discrete-time Markov chains; Reneval theory; Poisson point processes; Brownian motion

• Prerequisites:

   

  Basic properties of measures, the integral with respect to Lebesgue measure, Lebesgue measure, sigma-algebras.

• Books:

   

  [1] R.M. Dudley. Real Analysis and Probability. Cambridge studies in advanced mathematics 74, 2002.
  [2] E. Hewitt and K. Stromberg, Real and Abstract Analysis. 1991. Springer.
  [3] W. Feller. An Introduction to Probability Theory and Its Applications. John Wiley & Sons, Inc, 1968.
  [4] P.G. Hoel, S.C. Port and C.J. Stone. Introduction to Probability Theory. Houghton Miin Company, 1971.
  [5] H.-H. Kuo. Introduction to Stochastic Integration. Springer, 2006.
  [6] D.C. Montgomery and G.C. Runger. Applied Statistics and Probability for Engineers. John Wiley & Sons, Inc., 2003.
  [7] S.H. Ross. Introduction to Probability Models. Academic Press, 2007.
  [8] H.L. Royden. Real Analysis. Third Edition. 1988. Prentice-Hall. Inc.
  [9] M. Sanz i Solé. Probabilitats. 1999. Universitat de Barcelona.
  [10] A.N. Shiryaev. Probability. 2000. Springer.
  [11] D. Williams. Probability with Martingales. Cambridge Mathematical Textbooks, 1991.