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Generalised transforms, quasi-diffusions, and Désiré André's equation

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Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1526)

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References

  1. Chung, K.L. and Fuchs, W.H.J.On the distribution of values of sums of random variables. Mem. AMS. 6 (1951) 1–12.

    MathSciNet  MATH  Google Scholar 

  2. Dym, H. and McKean, H.P.Gaussian processes, function theory, and the inverse spectral problem. Academic Press, London and New York, 1976.

    MATH  Google Scholar 

  3. Küchler, U.Some asymptotic properties of the transition densities of one-dimensional quasi-diffusions. Publ. RIMS Kyoto 16 (1980) pp 245–268.

    CrossRef  MATH  Google Scholar 

  4. Küchler, U. and Salminen, P.On spectral measures of strings and excursions of quasi-diffusions. Séminaire de Probabilités XXIII, Springer Lecture Notes No. 1372 (1989) 490–502.

    MATH  Google Scholar 

  5. London R.R., McKean H.P., Rogers L.C.G., Williams D.A martingale approach to some Wiener-Hopf Problems I. Séminaire de Probabilités XVI, Springer Lecture Notes No. 920 (1982) 41–67.

    MathSciNet  Google Scholar 

  6. Maisonneuve, B.Exit systems. Ann. Prob. 3, (1975) 399–411.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. McGill, P.Wiener-Hopf factorisation of Brownian motion. Prob. Th. Rel. Fields. 83, (1989) 355–389.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. McGill, P.Some eigenvalue identities for Brownian motion. Proc.Camb.Phil.Soc. 105 (1989) 587–596.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Ray D.B.Stable processes with absorbing barrier. Trans. Amer. Math. Soc. 89 (1958) 16–24.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Revuz D. and Yor M.Continuous martingales and Brownian motion. Springer-Verlag, New York and Heidelberg, 1991.

    CrossRef  MATH  Google Scholar 

  11. Rogers, L.C.G.A diffusion first passage problem. Seminar on Stochastic Processes, 1983, Birkhäuser, Boston (1984) pp 151–160.

    CrossRef  Google Scholar 

  12. Rogozin, B. A.On the distribution of functionals related to boundary problems for processes with independent increments. Theory Prob. Appl. 11 (1966) 580–591.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Williams D.Some aspects of Wiener-Hopf factorization. Phil. Trans. R. Soc. Lond. A. 335 (1991) 593–608.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1992 Springer-Verlag

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McGill, P. (1992). Generalised transforms, quasi-diffusions, and Désiré André's equation. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXVI. Lecture Notes in Mathematics, vol 1526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084325

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  • DOI: https://doi.org/10.1007/BFb0084325

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  • Print ISBN: 978-3-540-56021-0

  • Online ISBN: 978-3-540-47342-8

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