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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
     

Strassen theorems for a class of iterated processes

Author(s): Endre Csáki; Antónia Földes; Pál Révész
Journal: Trans. Amer. Math. Soc. 349 (1997), 1153-1167.
MSC (1991): Primary 60J65; Secondary 60F15, 60F17
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Abstract: A general direct Strassen theorem is proved for a class of stochastic processes and applied for iterated processes such as $W(L_t)$, where $W(\cdot )$ is a standard Wiener process and $L_.$ is a local time of a Lévy process independent from $W(\cdot )$.


References:

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. Csörg\H{o}, 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. Csörg\H{o}, A. Földes and P. Révész, Strong approximation of additive functionals, J. Theor. Probab. 5 (1992), 679-706. MR 93k:60073
7.
E. Csáki, M. Csörg\H{o}, 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. Csörg\H{o} 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 Csörg\H{o}-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


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Additional Information:

Endre Csáki
Affiliation: Mathematical Institute of the Hungarian Academy of Sciences, Budapest, P.O.B. 127, H-1364, Hungary
Email: csaki@novell.math-inst.hu

Antónia Földes
Affiliation: College of Staten Island, CUNY, 2800 Victory Blvd., Staten Island, New York 10314
Email: foldes@postbox.csi.cuny.edu

Pál Révész
Affiliation: Institut für Statistik und Wahrscheinlichkeitstheorie, Technische Universität Wien, A-1040 Wien, Austria
Email: revesz@ci.tuwien.ac.at

DOI: 10.1090/S0002-9947-97-01717-0
PII: S 0002-9947(97)01717-0
Keywords: Iterated Brownian motions, iterated processes, Strassen method, local times
Received by editor(s): August 3, 1995
Additional Notes: The first author was supported by the Hungarian National Foundation for Scientific Research, Grant No. T 016384 and T 019346
The second author was supported by a PSC CUNY Grant, No. 6-663642
Copyright of article: Copyright 1997, American Mathematical Society


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