Probability and stochastic processes
Additional Info
- ECTS credits: 6
- University: Autonomous University of Barcelona
- Semester: 3
- Lecturer 1: Vicenç MÉNDEZ
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Objectives:
The main goal is to provide powerful tools to deal with the analysis and numerical simulations of stochasticity both for systems affected by external noise or by internal noise. Applications to ecological or biological systems will be discussed in detail.
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Topics:
Probability spaces. Stochastic processes. Markov processes. Microscopic description with stochastic differential equations. Mesoscopic description with the master equation and diffusions. Anomalous diffusions. Simulation of stochastic processes.
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Prerequisites:
Basic properties of measures, the integral with respect to Lebesgue measure, Lebesgue measure, sigma-algebras.
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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.
