Advertisement

Heuristic Definitions

  • Nicola Cufaro PetroniEmail author
Chapter
  • 69 Downloads
Part of the UNITEXT for Physics book series (UNITEXTPH)

Abstract

At this stage of the presentation we will introduce the Poisson process by first explicitly producing its trajectories, and then by analyzing its probabilistic properties. This illuminating and informative procedure, however, can not be easily replicated for other typical, non trivial processes whose trajectories, as we will see later, can only be defined either as limits of suitable approximations or by adopting a more general standpoint

References

  1. 1.
    Papoulis, A.: Probability, Random Variables and Stochastic Processes. McGraw Hill, Boston (2002)zbMATHGoogle Scholar
  2. 2.
    Brown, R.: A brief account of microscopical observations made in the months of June, July and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. Phil. Mag. 4, 161 (1828)CrossRefGoogle Scholar
  3. 3.
    Einstein, A.: Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. Phys. 17, 549 (1905)CrossRefGoogle Scholar
  4. 4.
    von Smoluchowski, M.: Zur kinetischen Theorie der Brownschen Molekularbewegung und der suspensionen. Ann. Phys. 21, 757 (1906)zbMATHGoogle Scholar
  5. 5.
    Perrin, J.: Mouvement brownien et réalité moléculaire. Ann. Chim. Phys. 8-ième série 18, 5 (1909)Google Scholar
  6. 6.
    Thiele, T.N.: Om Anvendelse af mindste Kvadraters Methode i nogle Tilfaelde, hvor en Komplikation af visse Slags uensartede tilfaeldige Fejlkilder giver Fejlene en “systematisk” Karakter, B. Lunos Kgl. Hof.-Bogtrykkeri, (1880)Google Scholar
  7. 7.
    Bachelier, L.: Théorie de la Spéculation. Ann. Sci. de l’É.N.S. \(3^e\) série, tome 17, 21 (1900)Google Scholar
  8. 8.
    Langevin, P.: On the theory of Brownian motion. C. R. Acad. Sci. (Paris) 146, 530 (1908)Google Scholar
  9. 9.
    Ornstein, L.S., Uhlenbeck, G.E.: On the theory of Brownian motion. Phys. Rev. 36, 823 (1930)ADSCrossRefGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of BariBariItaly

Personalised recommendations