Moderate deviations and functional LIL for super-Brownian motion

Stochastic Processes and their Applications

Volumn 72, Issue 1, 1997, Pages 11-25

  Schied, Alexander ^a  

^a HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Functional central limit theorem; H lder space; Moderate deviations; Orlicz space; Strassen type law of the iterated logarithm; Uniform large deviations

Indexed keywords

EID: 0031536934     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(97)00078-1     Document Type: Article

References (18)

1. Castaing, C., Valadier, M., 1977. Convex Analysis and Measurable Multifunctions, Springer, Berlin.
2. Dawson, D.A., 1993. Measure-valued Markov processes. In: Hennequin, P.L. (Ed.), Ecole d' Eté de Probabilités de Saint-Flour XXI, Lect. Notes Math., vol. 1541. Springer, Berlin, pp. 1-260.
3. Dellacherie, C., Meyer, P.-A., 1980. Probabilités et Potentiel, Chapitres V à VIII. Hermann, Paris.
4. Dembo, A., Zajic, T., 1995. Uniform large and moderate deviations for functional empirical processes. Preprint.
5. Dembo, A., Zeitouni, O., 1993. Large Deviation Techniques. Jones and Bartlett Publishers, Boston.
6. Deuschel, J.D., Stroock, D.W., 1989. Large Deviations. Academic Publishers, Boston.
7. Deuschel, J.D., Wang, K., 1993. Large deviations for occupation time functionals of branching Brownian particles and super-Brownian motion. Preprint, ETH Zürich.
8. Dudley, R.M., 1966. Convergence of Baire measures. Studia Math. 27; 251-268.
9. Fleischmann, K., Gärtner, J., Kaj, I., 1996. A Schilder type theorem for super-Brownian motion. Can. J. Math. 48; 542-568.
10. Gantert, N., 1993. An inversion of Strassen's law of the iterated logarithm for small time. Ann. Probab. 21; 1045-1049.
11. Jakubowski, A., 1986. On the Skorohod topology. Ann. Inst. H. Poincaré B 22; 263-285.
12. Mueller, C., 1983. A unification of Strassen's law and Levy's modulus of continuity. Z. Wahrscheinlichkeitstheorie Verw. Geb. 56; 163-179.
13. Revuz, D., Yor, M., 1994. Continuous Martingales and Brownian Motion. Springer, Berlin.
14. Schied, A., 1995. Große Abweichungen für die Pfade der Super-Brownschen Bewegung. Bonner Math. Schriften 277; 1-91.
15. Schied, A., 1996. Sample path large deviations for super-Brownian motion. Probab. Theory Related Fields 104; 319-347.
16. Serlet, L. 1997. A large deviation principle for the Brownian snake. Stoch. Proc. Appl. 67, 101-115.
17. Strassen, V. 1964. An invariance principle for the law of the iterated logarithm. Z. Wahrsch. verw. Gebiete 3; 211-226.
18. Wu, L., 1994. Large deviations, moderate deviations and LIL for empirical processes. Ann. Probab. 22; 17-27.