We assume that the reader is already familiar with the basic motivations and notions of probability theory. In this chapter we recall the main mathematical concepts, methods, and theorems according to the Kolmogorov approach Kolmogorov (1956) by using as main references the books by Métivier (1968) and Neveu (1965). An interesting introduction can be found in Gnedenko (1963). We shall refer to Appendix A of this book for the required theory on measure and integration.


  1. Applebaum, D.: Levy Processes and Stochastic Calculus. Cambridge University Press, Cambridge (2004)Google Scholar
  2. Ash, R.B.: Real Analysis and Probability. Academic, London (1972)Google Scholar
  3. Bauer, H.: Probability Theory and Elements of Measure Theory. Academic, London (1981)Google Scholar
  4. Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1968)Google Scholar
  5. Billingsley, P.: Probability and Measure. Wiley, New York (1986)Google Scholar
  6. Bohr, H.: Almost Periodic Functions. Chelsea, New York (1947)Google Scholar
  7. Chow, Y.S., Teicher, H.: Probability Theory: Independence, Interchangeability, Martingales. Springer, New York (1988)Google Scholar
  8. Chung, K.L.: A Course in Probability Theory, 2nd edn. Academic, New York (1974)Google Scholar
  9. Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications. Corrected printing. Springer, Heidelberg (2010)Google Scholar
  10. Fristedt, B., Gray, L.: A Modern Approach to Probability Theory. Birkhäuser, Boston (1997)Google Scholar
  11. Gnedenko, B.V.: The Theory of Probability. Chelsea, New York (1963)Google Scholar
  12. Jacod, J., Protter, P.: Probability Essentials. Springer, Heidelberg (2000)Google Scholar
  13. Jeanblanc, M., Yor, M., Chesney, M.: Mathematical Methods for Financial Markets. Springer, London (2009)Google Scholar
  14. Khinchin, A.I.: Mathematical Foundations of Information Theory. Dover, New York (1957)Google Scholar
  15. Klenke, A.: Probability Theory. Springer, Heidelberg (2008)Google Scholar
  16. Kolmogorov, A.N.: Foundations of the Theory of Probability. Chelsea, New York (1956)Google Scholar
  17. Loève, M.: Probability Theory. Van Nostrand-Reinhold, Princeton, NJ (1963)Google Scholar
  18. Lukacs, E.: Characteristic Functions. Griffin, London (1970)Google Scholar
  19. Métivier, M.: Notions fondamentales de la théorie des probabilités. Dunod, Paris (1968)Google Scholar
  20. Neveu, J.: Mathematical Foundations of the Calculus of Probability. Holden-Day, San Francisco (1965)Google Scholar
  21. Samorodnitsky, G., Taqqu, M.S.: Stable Non-Gaussian Random Processes. Chapman & Hall/CRC Press, Boca Ration, FL (1994)Google Scholar
  22. Sato, K.I.: Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge (1999)Google Scholar
  23. Shiryaev, A.N.: Probability. Springer, New York (1995)Google Scholar
  24. Tucker, H.G.: A Graduate Course in Probability. Academic Press, New York (1967)Google Scholar
  25. Williams, D.: Probability with Martingales. Cambridge University Press, Cambridge (1991)Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Vincenzo Capasso
    • 1
  • David Bakstein
    • 1
  1. 1.ADAMSS (Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences)Università degli Studi di MilanoMilanItaly

Personalised recommendations