Brownian local times and branching processes

L. C. G. Rogers

Séminaire de probabilités de Strasbourg (1984)

  • Volume: 18, page 42-55

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Rogers, L. C. G.. "Brownian local times and branching processes." Séminaire de probabilités de Strasbourg 18 (1984): 42-55. <http://eudml.org/doc/113496>.

@article{Rogers1984,
author = {Rogers, L. C. G.},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {critical branching process; Bessel process; local time of Brownian motion},
language = {eng},
pages = {42-55},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Brownian local times and branching processes},
url = {http://eudml.org/doc/113496},
volume = {18},
year = {1984},
}

TY - JOUR
AU - Rogers, L. C. G.
TI - Brownian local times and branching processes
JO - Séminaire de probabilités de Strasbourg
PY - 1984
PB - Springer - Lecture Notes in Mathematics
VL - 18
SP - 42
EP - 55
LA - eng
KW - critical branching process; Bessel process; local time of Brownian motion
UR - http://eudml.org/doc/113496
ER -

References

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  1. [1] Athreya, K.B. and Ney, P.E.Branching Processes. Springer, Berlin, 1972. Zbl0259.60002MR373040
  2. [2] Billingsley, P.Convergence of Probability Measures. Wiley, New York, 1968. Zbl0172.21201MR233396
  3. [3] Durrett, R.Conditioned limit theorems for some null recurrent Markov processes. Ann. Probability6, 798-828, 1978. Zbl0398.60023MR503953
  4. [4] Durrett, R. and Resnick, S.I.Functional limit theorems for dependent variables. Ann. Probability6, 829-846, 1978. Zbl0398.60024MR503954
  5. [5] Dwass, M.Branching processes in simple random walk. Proc. Amer. Math. Soc.51, 270-274, 1975. Zbl0312.60032MR370775
  6. [6] Ikeda, N. and Watanabe, S.Stochastic differential equations and diffusion processes. North Holland-Kodansha, Amsterdam and Tokyo, 1981. Zbl0495.60005MR637061
  7. [7] Jacod, J. Memin, J., and Metivier, M.Stopping times and tightness. Stoch. Procs. and App.14, 109-146, 1982. Zbl0501.60029
  8. [8] Knight, F.B.Random walks and a sojourn density of Brownian motion. Trans. Amer. Math. Soc.109, 56-86, 1963. Zbl0119.14604MR154337
  9. [9] Lamperti, J.The limit of a sequence of branching processes. Z.f. Wahrscheinlichkeitsth.7, 271-288, 1967. Zbl0154.42603MR217893
  10. [10] Lindvall, T.Convergence of critical Galton-Watson processes. J. Appl. Probability9, 445-450, 1972. Zbl0238.60063MR345227
  11. [11] Pitman, J.W. and Yor, M.Bessel processes and infinitely divisible laws. Stochastic Integrals SLN851, 285-370, Ed. D. Williams. Springer, Berlin, 1981. Zbl0469.60076MR620995
  12. [12] Pitman, J.W. and Yor, M.A decomposition of Bessel bridges. Z.f. Wahrscheinlichkeitsth.59, 425-457, 1982. Zbl0484.60062MR656509
  13. [13] Ray, D.B.Sojourn times of diffusion processes. I11 J. Math.7, 615-630, 1963. Zbl0118.13403MR156383
  14. [14] Rogers, L.C.G.Williams' characterisation of the Brownian excursion law; proof and applications. Sem. Prob.XV227-250, Springer, Berlin,1981. Zbl0462.60078MR622566
  15. [15] Williams, D.Diffusions, Markov Processes, and Martingales. Vol. I. Wiley, Chichester1979. Zbl0402.60003MR531031
  16. [16] Yamada, T. and Watanabe, S.. On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ.11, 155-167, 1971. Zbl0236.60037MR278420

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