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Brownian Motions on a Half Line

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Part of the Contemporary Mathematicians book series (CM)

Abstract

‘Numbering (in italics). (1) means formula 1 in the present section; (2.1) means formula (1) of Section 15.2, etc.’

Keywords

Brownian Motion Local Time Sample Path Green Operator Standard Brownian Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [1]
    J. L. Doob. Stochastic processes. John Wiley & Sons Inc., New York, 1953.zbMATHGoogle Scholar
  2. [2]
    E. B. Dynkin. Infinitessimal operators of Markov processes (Russian). Teor. Veroyatnost. i Primenen, 1:38–60, 1956.MathSciNetzbMATHGoogle Scholar
  3. [3]
    W. Feller. The parabolic differential equations and the associated semi-groups of transformations. Ann. of Math., 55:468–519, 1952.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    W. Feller. Diffusion processes in one dimension. Trans. Amer. Math. Soc., 77:1–31, 1954.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    W. Feller. Generalized second order differential operators and their lateral conditions. Illinois J. Math., 1:459–564, 1957.MathSciNetzbMATHGoogle Scholar
  6. [6]
    W. Feller. The birth and death processes as diffusion processes. J. Math. Pures Appl., 38:301–345, 1959.MathSciNetzbMATHGoogle Scholar
  7. [7]
    G. Hunt. Some theorems concerning Brownian motion. Trans. AMS, 81:294–319, 1956.CrossRefzbMATHGoogle Scholar
  8. [8]
    K. Itô. On stochastic processes. I. (Infinitely divisible laws of probability). Jap. J. Math., 18:261–301, 1942.Google Scholar
  9. [9]
    K. Itô and H. P. McKean. Diffusion Processes and Their Sample Paths. Academic Press, 1965.CrossRefzbMATHGoogle Scholar
  10. [10]
    M. Kac. On some connections between probability theory and differential and integral equations. In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, pages 189–215. University of California Press, 1951.Google Scholar
  11. [11]
    P. Lévy. Sur les intègrales dont les èlèments sont des variables alèatoires indèpendantes. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2), 3(3–4):337–366, 1934.MathSciNetGoogle Scholar
  12. [12]
    P. Lévy. Sur certains processus stochastiques homogènes. Compositio Math., 7:283–339, 1940.Google Scholar
  13. [13]
    P. Lévy. Processus Stochastiques et Mouvement Brownien. Gauthier-Villars, Paris, 1948.zbMATHGoogle Scholar
  14. [14]
    D. B. Ray. Resolvents, transition functions, and strongly Markovian processes. Ann. of Math., 70:43–72, 1959.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    A. V. Skorohod. Stochastic equations for diffusion processes with a boundary. Teor. Verojatnost. i Primenen, 6:287–298, 1961.MathSciNetGoogle Scholar
  16. [16]
    A. V. Skorohod. Stochastic equations for diffusion processes with boundaries. II. Teor. Verojatnost. i Primenen, 7:5–25, 1962.Google Scholar
  17. [17]
    H. F. Trotter. A property of Brownian motion paths. Illinois J. Math., 2:425–433, 1958.MathSciNetzbMATHGoogle Scholar
  18. [18]
    A. D. Ventcel’. Semigroups of operators that correspond to a generalized differential operator of second order (Russian). Dokl. Akad. Nauk SSSR, 111:269–272, 1956.Google Scholar
  19. [19]
    V. A. Volkonskii. Random time substitution in strong Markov processes. Teor. Veroyatnost. i Prim., 3:332–350, 1958.MathSciNetGoogle Scholar
  20. [20]
    N. Wiener. Differential space. J. Math. Phys., 2:131–174, 1923.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Courant InstituteNew York UniversityNew YorkUSA

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