Potential Analysis

, Volume 8, Issue 1, pp 61–68

Characteristic Functions and Symbols in the Theory of Feller Processes

  • Niels Jacob
Article

Abstract

We derive a probabilistic expression for the symbol of the generator of a Feller process.

Feller process characteristic function symbol of a pseudo differential operator 

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References

  1. 1.
    Berg, C. and Forst, G.: ‘Potential theory on locally compact Abelian groups’, Ergebnisse der Mathematik und ihrer Grenzgebiete, II. Ser. 87, Springer-Verlag, Berlin, 1975.Google Scholar
  2. 2.
    Courrège, P.: ‘Sur la forme intégro-différentielle des opérateurs de C k dans C satisfaisant au principe du maximum’, Sém. Théorie du Potentiel (1965/66) 38p.Google Scholar
  3. 3.
    Fukushima, M., Oshima, Y. and Takeda, M.: ‘Dirichlet forms and symmetric Markov processes’, De Gruyter Studies in Mathematics, 19, Walter de Gruyter, Berlin, 1994.Google Scholar
  4. 4.
    Garroni, M. G. and Menaldi, J. F.: ‘Green functions for second order parabolic integro-differential problems’, Pitman Research Notes in Mathematics, 275, Longman Scientific and Technical, Harlow, 1992.Google Scholar
  5. 5.
    Hoh, W.: ‘Pseudo differential operators with negative definite symbols and the martingale problem’, Stoch. Stoch. Rep. 55 (1995), 225-252.Google Scholar
  6. 6.
    Jacob, N.: ‘A class of Feller semigroups generated by pseudo differential operators’, Math. Z. 215 (1994), 151-166.Google Scholar
  7. 7.
    Taira, K.: Diffusion processes and partial differential equations, Academic Press, New York, 1988.Google Scholar
  8. 8.
    Von Waldenfels, W.: ‘Eine Klasse stationärer Markowprozesse’, Berichte der Kernforschungsanlage Jülich (1961).Google Scholar
  9. 9.
    Von Waldenfels, W.: ‘Positive Halbgruppen auf einem n-dimensionalen Torus’, Arch. Math. 15 (1964), 191-203.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Niels Jacob
    • 1
  1. 1.Institut für MathematikUniversität Erlangen-Nürnberg, BismarckstraβeErlangenGermany

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