The large deviation principle for stochastic processes. Part I

Theory of Probability and its Applications

Volumn 47, Issue 4, 2003, Pages 567-583

  Arcones, M A ^a  

^a BINGHAMTON UNIVERSITY   (United States)

Author keywords

Gaussian processes; Iterated Brownian motion; Large deviations; Poisson process; Stochastic processes

Indexed keywords

EID: 0942268012     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0040585X97980038     Document Type: Article

References (35)

1. M. A. ARCONES, The large deviation principle for stochastic processes, Part II, Theoret. Probab. Appl., 48 (2003), to appear.
2. M. A. ARCONES, On the law of the iterated logarithm for Gaussian processes, J. Theoret. Probab., 8 (1995), pp. 877-903.
3. M. A. ARCONES, Weak convergence of convex stochastic processes, Statist. Probab. Lett., 37 (1998), pp. 171-182.
4. R. R. BAHADUR, Some Limit Theorems in Statistics, SIAM, Philadelphia, 1971.
5. N. H. BINGHAM, C. M. GOLDIE, AND J. L. TEUGELS, Regular Variation, Cambridge University Press, Cambridge, UK, 1987.
6. C. BORELL, The Brunn-Minkowski inequality in Gauss space, Invent. Math., 30 (1975), pp. 207-216.
7. K. BURDZY, Some path properties of iterated Brownian motion, in Seminar on Stochastic Processes (Seattle, WA, 1992), Progr. Probab. 33, Birkhäuser, Boston, 1993, pp. 67-87.
8. K. BURDZY, Variation of iterated Brownian motion, in Measure-Valued Processes, Stochastic Partial Differential Equations, and Interacting Systems, CRM Proc. Lecture Notes 5, D. A. Dawson, ed., AMS, Providence, RI, 1994, pp. 35-53.
9. S. CHEVET, Gaussian measures and large deviations, in Probability in Banach Spaces IV, Proc. Semin., Oberwolfach, 1982, Lecture Notes in Math. 990, Springer-Verlag, Berlin, Heidelberg, 1983, pp. 30-46.
10. E. CSÁKI, M. CSÖRGÖ, A. FÖLDES, AND P. RÉVÉSZ, Global Strassen-type theorems for iterated Brownian motions, Stochastic Process. Appl., 59 (1995), pp. 321-341.
11. E. CSÁKI, A. FÖLDES, AND P. RÉVÉSZ, Strassen theorems for a class of iterated processes, Trans. Amer. Math. Soc., 349 (1997), pp. 1153-1167.
12. P. DEHEUVELS AND D. M. MASON, A functional L.I.L. approach to pointwise Bahadur-Kiefer theorems, in Probability in Banach Spaces 8: Proceedings of the Eighth International Conference, R. M. Dudley et al., eds., Birkhäuser, Boston, 1992, pp. 255-266.
13. A. DEMBO AND O. ZEITOUNI, Large Deviations Techniques and Applications, Springer-Verlag, New York, 1998.
14. J.-D. DEUSCHEL AND D. W. STROOCK, Large Deviations, Academic Press, Boston, MA, 1989.
15. M. D. DONSKER AND S. R. S. VARADHAN, Asymptotic evaluation of certain Markov process expectations for large time. III, Comm. Pure Appl. Math., 29 (1976), pp. 389-461.
16. R. M. DUDLEY, Uniform Central Limit Theorems, Cambridge University Press, Cambridge, UK, 1999.
17. N. DUNFORD AND J. T. SCHWARTZ, Linear Operators. Part I: General Theory, Wiley, New York, 1988.
18. R. S. ELLIS, Large deviations for a general class of random vectors, Ann. Probab., 12 (1984), pp. 1-12.
19. T. FUNAKI, Probabilistic construction of the solution of some higher order parabolic differential equations, Proc. Japan Acad., 55 (1979), pp. 176-179.
20. J. HOFFMANN-JøRGENSEN, Stochastic Processes on Polish Spaces, Various Publications Ser. 39, Aarhus University, Aarhus, Denmark, 1991.
21. Y. HU AND Z. SHI, The Csörgö-Révész modulus of non-differentiability of iterated Brownian motion, Stochastic Process. Appl., 58 (1995), pp. 267-279.
22. Y. HU, D. PIERRE-LOTI-VIAUD, AND Z. SHI, Laws of the iterated logarithm for iterated Wiener processes, J. Theoret. Probab., 8 (1995), pp. 303-319.
23. D. KHOSHNEVISAN AND T. M. LEWIS, The uniform modulus of continuity of iterated Brownian motion, J. Theoret. Probab., 9 (1996), pp. 317-333.
24. D. KHOSHNEVISAN AND T. M. LEWIS, Chung's law of the iterated logarithm for iterated Brownian motion, Ann. Inst. H. Poincaré Probab. Statist., 32 (1996), pp. 349-359.
25. J. LYNCH AND J. SETHURAMAN, Large deviations for processes with independent increments, Ann. Probab., 15 (1987), pp. 610-627.
26. A. PUHALSKII, On functional principle of large deviations, in New Trends in Probability and Statistics (Bakuriani, 1990), Vol. 1, VSP, Utrecht, 1991, pp. 198-218.
27. M. M. RAO AND Z. D. REN, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991.
28. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
29. M. SÑHILDER, Some asymptotic formulas for Wiener integrals, Trans. Amer. Math. Soc., 134 (1966), pp. 193-216.
30. Z. SHI, Lower limits of iterated Wiener processes, Statist. Probab. Lett., 23 (1995), pp. 259-270.
31. V. N. SUDAKOV AND B. S. CIREL'SON, Extremal properties of half-spaces for spherically invariant measures. Problems in the theory of probability distributions. II, Zap. Naučhn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 41 (1974), pp. 14-24 (in Russian).
32. A. W. VAN DER VAART AND J. A. WELLNER, Weak Convergence and Empirical Processes. With Applications to Statistics, Springer-Verlag, New York, 1996.
33. S. R. S. VARADHAN, Asymptotic probabilities and differential equations, Comm. Pure Appl. Math., 19 (1966), pp. 261-286.
34. S. R. S. VARADHAN, Large Deviations and Applications, SIAM, Philadelphia, 1984.
35. S. WILLARD, General Topology, Addison-Wesley, Reading, MA, 1970.