On spectral measures of strings and excursions of quasi-diffusions

Uwe Küchler; Paavo Salminen

Séminaire de probabilités de Strasbourg (1989)

  • Volume: 23, page 490-502

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Küchler, Uwe, and Salminen, Paavo. "On spectral measures of strings and excursions of quasi-diffusions." Séminaire de probabilités de Strasbourg 23 (1989): 490-502. <http://eudml.org/doc/113697>.

@article{Küchler1989,
author = {Küchler, Uwe, Salminen, Paavo},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {quasi diffusions; spectral theory of strings; excursion theory of quasi diffusions; spectral representations; inverse local times},
language = {eng},
pages = {490-502},
publisher = {Springer - Lecture Notes in Mathematics},
title = {On spectral measures of strings and excursions of quasi-diffusions},
url = {http://eudml.org/doc/113697},
volume = {23},
year = {1989},
}

TY - JOUR
AU - Küchler, Uwe
AU - Salminen, Paavo
TI - On spectral measures of strings and excursions of quasi-diffusions
JO - Séminaire de probabilités de Strasbourg
PY - 1989
PB - Springer - Lecture Notes in Mathematics
VL - 23
SP - 490
EP - 502
LA - eng
KW - quasi diffusions; spectral theory of strings; excursion theory of quasi diffusions; spectral representations; inverse local times
UR - http://eudml.org/doc/113697
ER -

References

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  1. [1] Csáki, E., Földes, A., Salminen, P.: On the joint distribution of the maximum and its location for a linear diffusion. Ann. Inst. H. Poincare Vol. 23(2), 1987, p. 179-194. Zbl0621.60081MR891709
  2. [2] Getoor, R.K.: Excursions of a Markov process. Ann. Prob.Vol. 7(2), 1979, p. 244-266. Zbl0399.60069MR525052
  3. [3] Dym, H., McKean, H.: Gaussian Processes, Function theory and Inverse Spectral Problem. Academic Press.New York (1976). Zbl0327.60029
  4. [4] Ito, K., McKean, H.: Diffusion Processes and their Sample Paths. Springer Verlag.Berlin (1965). Zbl0127.09503
  5. [5] Kac, I.S., Krein, M.G.: On the spectral functions of the string. Amer. Math. Soc. Transl.II Ser. 103, 1974, p. 19-102. Zbl0291.34017
  6. [6] Kac, I.S., Krein, M.G.: R-functions - analytic functions mapping the upper half plane into itself. Amer. Mat. Soc. Transl.II Ser. 103, 1974, p. 1-18. Zbl0291.34016
  7. [7] Kent, J.T.: Eigenvalue expansions for diffusion hitting times. Z. Wahrscheinlichkeitstheorie verw. Gebiete52, 1980, p. 309-319. Zbl0415.60071MR576891
  8. [8] Kent, J.T.: The spectral decomposition of a diffusion hitting time. Ann. Prob.10, 1982, p. 207-219. Zbl0483.60075MR637387
  9. [9] Knight, F.B.: Characterization of the Levy measures of inverse local times of gap diffusion. In Seminar on Stochastic Processes, 1981, ed. Cinlar, E., Chung, K.L., Getoor, R.K Progress in Probability and Statistics, Birkhäuser, Boston (1981). Zbl0518.60083MR647781
  10. [10] Kotani, S., Watanabe, S.: Krein's spectral theory of strings and generalized diffusion processes. In Functional Analysis in Markov Processes, ed. Fukushima, M. Lect. notes in math., 923, Springer Verlag, Berlin (1981). Zbl0496.60080MR661628
  11. [11] Küchler, U.: On sojourn times, excursions and spectral measures connected with quasi diffusions. J. Math. Kyoto Univ., 26(3), 1986, p. 403-421. Zbl0625.60093MR857226
  12. [12] Pitman, J., Yor, M.: A decomposition of Bessel bridges. Z. Wahrscheinlichkeitstheorie verw. Gebiete59, 1982, p. 425-457. Zbl0484.60062MR656509
  13. [13] Salminen, P.: Brownian excursions revisited. In Seminar on Stochastic Processes, 1983, ed Cinlar, E., Chung, K.L., Getoor, R.K Progress in Probability and Statistics7, Birkhäuser, Boston (1984) Zbl0557.60067MR902418
  14. [14] Williams, D.: Diffusions, Markov Processes and Martingales. Wiley and Sons, London (1979). Zbl0402.60003MR531031

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