Abstract
The role of correlation inequalities and martingale arguments in establishing conditional exponential bounds is reviewed. Applications to the computation of the Onsager Machlup functional for diffusions under non supremum norms follow.
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References
Baldi, P., Ben Arous, G. and Kerkyaacharian, G., “Large deviations and Strassen theorem in Hölder norm”. Preprint, 1991.
Carmona, R. and Nualart, D., “Traces of random variables on the Wiener space and the Onsager Machlup functional”, J. Functional Analysis, 107 (1992), pp. 402–438.
Chaleyat-Maurel, M. and Nualart, D., “The Onsager Machlup functional for a class of anticipating processes”, preprint (1991).
Ciesielski, Z., “On the isomorphism of the spaces Hα and m”, Bull de LÁcademie Pol. des Sciences, Serie des sci. math., astr., phys., VIII(1960), pp. 217–222.
Das Gupta S., Eaton M.L., Olkin L, Perlman M., Savage L.J. and Sobel M., “Inequalities on the probability content of convex regions for elliptically contoured distributions”, Sixth Berkeley symposium on Mathematical Statistics and Probability, vol II., 1972, pp. 241–265.
Fujita, J. and Kotani, S., “The Onsager Machlup function for diffusion processes”, J. Math. Kyoto Univ., 22 (1982), pp. 115–130.
Ikeda, N. and Watanabe, S., Stochastic Differential Equations and Diffusion Processes, 2nd edition, North-Holland, 1989.
Mayer-Wolf, E. and Zeitouni, O., “The probability of small Gaussian ellipsoids and associated exponential moments”, to appear, Annals of Probability (1992).
Mayer-Wolf, E. and Zeitouni, O., “Onsager-Machlup functional for non trace class SPDEs”, to appear, PTRF (1992).
Millet, A. and Nualart, D., “Theoreme de support pour une classe d’equations differentielles stochastiques anticipantes”, C.R. Acad. Sci. Paris, t. 312, Serie I (1991), pp. 743–746.
Onsager, L. and Machlup, S., “Fluctuations and irreversible processes”, I,II, Phys. Rev., 91 (1953), pp. 1505–1515.
Shepp, L.A. and Zeitouni, O., “A note on conditional exponential moments and the Onsager Machlup functional”, Annals of Probability, 20 (1992), pp. 652–654.
Stratonovich, R.L., “On the probability functional of diffusion processes”, Selected Trans, in Math. Stat. Prob., 10 (1971), pp. 273–286.
Sugita, H., “Various topologies in the Wiener space and Lévy’s stochastic area”, PTRF 91 (1992), pp. 283–296.
Takahashi, Y. and Watanabe, S., “The probability functional (Onsager-Machlup function) of diffusion processes”, Stochastic Integrals (D. Williams, Ed.), Lecture Notes in Math., 851 (1981), pp. 433–463. Springer, Berlin — New-York.
Wong, E. and Zakai, M., “On the relation between ordinary and stochastic differential equations”, Int. Jour. Eng. Sc., 3 (1965), pp. 213–229.
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Shepp, L.A., Zeitouni, O. (1993). Exponential estimates for convex norms and some applications. In: Nualart, D., Solé, M.S. (eds) Barcelona Seminar on Stochastic Analysis. Progress in Probability, vol 32. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8555-3_11
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DOI: https://doi.org/10.1007/978-3-0348-8555-3_11
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