Strassen theorems for a class of iterated processes

Transactions of the American Mathematical Society

Volumn 349, Issue 3, 1997, Pages 1153-1167

  Csáki, Endre ^a   Földes, Antónia ^b   Révész, Pál ^c  

^a ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS   (Hungary)

^b CITY UNIVERSITY OF NEW YORK   (United States)

^c VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Iterated brownian motions; Iterated processes; Local times; Strassen method

Indexed keywords

EID: 21744446851     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-97-01717-0     Document Type: Article

References (20)

1. M. A. Arcones, On the law of the iterated logarithm for Gaussian processes and their compositions, J. Theor. Probab. 8 (1995), 877-903. CMP 96:2
2. J. Bertoin, Iterated Brownian motion and stable (1/4) subordinator, Statist. Probab. Letters 27 (1996), 111-114.
3. K. Burdzy, Some path properties of iterated Brownian motion, in: E. Çinlar, K.L. Chung and M. Sharpe, eds., Seminar on Stochastic Processes (Birkhäuser, Boston, 1993), pp. 67-87. MR 95c:60075
4. K. Burdzy, Variation of iterated Brownian motion, in: D.A. Dawson, ed., Measure-Valued Processes, Stochastic Partial Differential Equations and Interacting Systems, CRM Proceedings & Lecture Notes, Vol. 5 (1994), 35-53. MR 95h:60123
5. E. Csáki, M. Csörgó, A. Földes and P. Révész, Brownian local time approximated by a Wiener sheet, Ann. Probab. 17 (1989), 516-537. MR 95h:60102
6. E. Csáki, M. Csörgó, A. Földes and P. Révész, Strong approximation of additive functionals, J. Theor. Probab. 5 (1992), 679-706. MR 93k:60073
7. E. Csáki, M. Csörgó, A. Földes and P. Révész, Global Strassen-type theorems for iterated Brownian motions, Stochastic Proc. Appl. 59 (1995), 321-341. CMP 96:3
8. M. Csörgó and P. Révész, Strong Approximations in Probability and Statistics (Academic Press, New York, 1981). MR 84d:60050
9. C. Dellacherie and P. A. Meyer, Probabilities and Potential, Vol. 1 (North-Holland, Amsterdam, 1978). MR 80b:60004
10. Y. Hu, D. Pierre-Loti-Viaud and Z. Shi, Laws of the iterated logarithm for iterated Wiener processes, J. Theor. Probab. 8 (1995), 303-319. MR 96b:60073
11. Y. Hu and Z. Shi, The Csörgó-Révész modulus of non-differentiability of iterated Brownian motion, Stochastic Proc. Appl. 58 (1995), 267-279. CMP 95:17
12. D. Khoshnevisan, The rate of convergence in the ratio ergodic theorem for Markov processes, Preprint, 1995.
13. D. Khoshnevisan and T. M. Lewis, The uniform modulus of continuity of iterated Brownian motion, J. Theor. Probab. 9 (1996), 317-333.
14. D. Khoshnevisan and T. M. Lewis, Chung's law of the iterated logarithm for iterated Brownian motion, Ann. Inst. H. Poincarè 32 (1996), 349-359.
15. D. Khoshnevisan, T. M. Lewis and Z. Shi, Upper functions of iterated Brownian motion, Preprint, 1994.
16. M. Marcus and J. Rosen, Laws of the iterated logarithm for the local times of symmetric Lévy processes and recurrent random walks, Ann. Probab. 22 (1994), 626-658. MR 95k:60190
17. Z. Shi, Lower limits of iterated Wiener processes, Statist. Probab. Letters 23 (1995), 259-270. CMP 95:15
18. Z. Shi, Liminf results for self-iterated Brownian motion, Preprint, 1994.
19. F. Riesz and B. Sz.-Nagy, Functional Analysis (Frederick Ungar, New York, 1955). MR 17:175i
20. V. Strassen, An invariance principle for the law of the iterated logarithm, Z. Wahrsch. Verw. Gebiete 3 (1964), 211-226. MR 30:5379