Hirsch's integral test for the iterated brownian motion

Jean Bertoin; Zhan Shi

Séminaire de probabilités de Strasbourg (1996)

  • Volume: 30, page 361-368

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Bertoin, Jean, and Shi, Zhan. "Hirsch's integral test for the iterated brownian motion." Séminaire de probabilités de Strasbourg 30 (1996): 361-368. <http://eudml.org/doc/113939>.

@article{Bertoin1996,
author = {Bertoin, Jean, Shi, Zhan},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {iterated Brownian motion; Hirsch's integral test; lower functions; extended Borel-Cantelli lemma},
language = {eng},
pages = {361-368},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Hirsch's integral test for the iterated brownian motion},
url = {http://eudml.org/doc/113939},
volume = {30},
year = {1996},
}

TY - JOUR
AU - Bertoin, Jean
AU - Shi, Zhan
TI - Hirsch's integral test for the iterated brownian motion
JO - Séminaire de probabilités de Strasbourg
PY - 1996
PB - Springer - Lecture Notes in Mathematics
VL - 30
SP - 361
EP - 368
LA - eng
KW - iterated Brownian motion; Hirsch's integral test; lower functions; extended Borel-Cantelli lemma
UR - http://eudml.org/doc/113939
ER -

References

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  2. Burdzy, K. (1993), Some path properties of iterated Brownian motion, in: E. Çinlar, K.L. Chung and M. Sharpe, eds, Seminar on stochastic processes 1992 (Birkhäuser) pp. 67-87. Zbl0789.60060MR1278077
  3. Burdzy, K. and Khoshnevisan, D. (1995), The level sets of iterated Brownian motion, Séminaire de Probabilités XXIX pp. 231-236, Lecture Notes in Math.1613, Springer. Zbl0853.60061MR1459464
  4. Csáki, E. (1978), On the lower limits of maxima and minima of Wiener process and partial sums, Z. Wahrscheinlichkeitstheorie verw. Gebiete43, 205-221. Zbl0372.60113MR494527
  5. Csáki, E., Csörgö, M., Földes, A. and Révész, P. (1989), Brownian local time approximated by a Wiener sheet, Ann. Probab.17, 516-537. Zbl0674.60072MR985376
  6. Csáki, E., Csörgö, M., Földes, A. and Révész, P. (1995), Global Strassen-type theorems for iterated Brownian motions, Stochastic Process. Appl.59, 321-341. Zbl0843.60072MR1357659
  7. Csáki, E., Földes, A. and Révész, P. (1995), Strassen theorems for a class of iterated processes, preprint. Zbl0867.60051MR1373631
  8. Deheuvels, P. and Mason, D.M. (1992), A functional LIL approach to pointwise Bahadur-Kiefer theorems, in: R.M. Dudley, M.G. Hahn and J. Kuelbs, eds, Probability in Banach spaces8 (Birkhäuser) pp. 255-266. Zbl0844.60012MR1227623
  9. Feller, W.E. (1971), An introduction to probability theory and its applications, 2nd edn, vol. 2. Wiley, New York. Zbl0219.60003
  10. Funaki, T. (1979), A probabilistic construction of the solution of some higher order parabolic differential equations, Proc. Japan Acad.55, 176-179. Zbl0433.35039MR533542
  11. Hu, Y., Pierre Loti Viaud, D. and Shi, Z. (1995), Laws of the iterated logarithm for iterated Wiener processes, J. Theoretic. Prob.8, 303-319. Zbl0816.60027MR1325853
  12. Hu, Y. and Shi, Z. (1995), The Csörgö-Révész modulus of non-differentiability of iterated Brownian motion, Stochastic Process. Appl.58, 267-279. Zbl0833.60033MR1348378
  13. Khoshnevisan, D. and Lewis, T.M. (1996), The uniform modulus of iterated Brownian motion, J. Theoretic. Prob. (to appear). Zbl0880.60081MR1385400
  14. Khoshnevisan, D. and Lewis, T.M. (1996), Chung's law of the iterated logarithm for iterated Brownian motion, Ann. Inst. Henri Poincaré (to appear) Zbl0859.60025MR1387394
  15. Pitman, J.W.and Yor, M. (1993). Homogeneous functionals of Brownian motion (unpublished manuscript). 
  16. Shi, Z. (1995), Lower limits of iterated Wiener processes, Statist. Probab. Letters. 23, 259-270. Zbl0824.60025MR1340161
  17. Spitzer, F. (1964). Principles of random walks. Van Nostrand, Princeton. Zbl0119.34304MR171290

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