Results in Mathematics

, Volume 21, Issue 3–4, pp 274–288 | Cite as

On martingales and feller semigroups

  • J. A. van Casteren
Results in Mathematics


Let E be a second countable locally compact Hausdorff space and let L be a linear operator with domain D(L) and range R(L) in C0(E). Suppose that D(L) is dense in E. The following assertions are equivalent:
  1. (a)

    For L the martingale problem is uniquely solvable and L is maximal for this property

  2. (b)

    The operator L generates a Feller semigroup in C0(E).



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  1. 1.
    H. Bauer, Probability theory and elements of measure theory, Holt, Rinehart and Winston Inc., New York 1972.Google Scholar
  2. 2.
    R.M. Blumenthal and R.K. Getoor, Markov processes and potential theory, Pure and Applied mathematics 29: a series of monographs and textbooks, Academic Press, New York 1986.Google Scholar
  3. 3.
    R. Durrett, Brownian motion and martingales in analysis, Wadsworth, Advanced Books and Software, Belmont 1984.Google Scholar
  4. 4.
    S.N. Ethier and T.G. Kurtz, Markov processes, characterization and convergence, Wiley Series in Probability and Statistics, John Wiley and Sons, New York 1985.Google Scholar
  5. 5.
    N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes second edition, North-Holland, Amsterdam 1989.MATHGoogle Scholar
  6. 6.
    T.M. Liggett, Interacting particle systems, Die Grundlehren der Mathematischen Wissenschaften 276, Springer Verlag, New York 1985.Google Scholar
  7. 7.
    D.W. Stroock and S.R.S. Varadhan, Multidimensional diffusion processes, Springer Verlag, Berlin 1979.MATHGoogle Scholar
  8. 8.
    J.A. van Casteren, Generators of strongly continuous semigroups, Research Notes in Mathematics 115, Pitman, London 1985.Google Scholar

Copyright information

© Birkhäuser Verlag, Basel 1992

Authors and Affiliations

  • J. A. van Casteren
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of Antwerp (UIA)Wilrijk/AntwerpBelgium

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