Abstract
For m≥1 let I m (h) denote the multiple Wiener-Itô integral of order m of a square integrable symmetric kernel h. In this paper we consider different conditions on a time-dependent family of kernels {h t , 0≤t≤1} which guarantee that the process I m (h t ) has continuous sample paths and that the probability measures induced by εm/2 I m (h t ) satisfy a large deviations principle in C([0,1]).
Keywords
- Multiple integral processes
- Large Deviations
- Hu-Meyer formula
- AMS 1985 Subject Classification
- 60F10
- 60G17
Partially supported by the Technion VPR Bernstein fund for the promotion of research
Partially supported by CONACYT, Grant A128CCOE900047 (MT-2)
Partially supported by CONACYT, Grant D111-904237
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References
R.C. Blei (1985): “Fractional dimensions and bounded fractional forms”, Mem. Amer. Math. Soc. 5, 331.
C. Borell (1978): “Tail probabilities in Gauss space”, in Vector space measures and applications, Dublin 1977, (L.N. Math. 644), pp. 73–82, Springer Berlin-Heidelberg-New York.
J.D. Deuschel and D.W. Stroock (1989): Large Deviations, Academic Press, New York.
X. Fernique (1983): “Regularite de fonctions aleatoires non Gaussiennes”, in Ecole d'Eté de Probabilités de Saint-Flour XI — 1981, (L.N. Math 976), pp. 1–74, P.L. Hennequin, ed., Springer Berlin-Heidelberg-New York.
Y.Z. Hu and P.A. Meyer (1988): “Sur les intégrales multiples de Stratonovich” in Séminaire de Probabilités XXII (L.N. Math. 1321), pp. 72–81, J. Azéma, P.A. Meyer and M. Yor, eds, Springer Berlin-Heidelberg-New York.
K. Itô (1951): “Multiple Wiener integrals”, J. Math. Soc. Japan, 3, pp. 157–169.
G.W. Johnson and G. Kallianpur (1989): “Some remarks on Hu and Meyer's paper and infinite dimensional calculus on finitely additive cannonical Hilbert space”, Th. Pr. Appl., 34, pp. 679–689.
M. Ledoux (1990): “A note on large deviations for Wiener chaos”, in Séminaire de Probabilités XXIV (L.N. Math. 1426), pp. 1–14, J. Azéma, P.A. Meyer and M. Yor, eds, Springer Berlin-Heidelberg-New York.
H.P. McKean (1973): “Wiener's theory of nonlinear noise”, in Stochastic Differential Equations, Proc. SIAM-AMS, 6, pp. 191–289.
T. Mori and H. Oodaira (1986): “The law of the iterated logarithm for self-similar processes represented bu multiple Wiener integrals”, Prob. Th. Rel. Fields, 71, pp. 367–391.
T. Mori and H. Oodaira (1988): “Freidlin-Wentzell type estimates and the law of the iterated logarithm for a class of stochastic processes related to symmetric statistics”, Yokohama Math. J., 36, pp. 123–130.
D. Nualart and M. Zakai (1990): “Multiple Wiener-Itô integrals possessing a continuous extension”, Prob. Th. Rel. Fields, 85, pp. 131–145.
A. Plikusas (1981): “Properties of the multiple Itô integral”, Lithuanian Math. J., 21, pp. 184–191.
L. C. G. Rogers and D. Williams (1987): Diffusions, Markov Processes, and Martingales, vol. 2, J. Wiley & Sons.
M. Schilder (1966): “Some asymptotic formulae for Wiener integrals”, Trans. Amer. Math. Soc., 125, pp. 63–85.
S.R.S. Varadhan (1984): Large Deviations and Applications CBMS series, SIAM, Philadelphia.
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© 1992 Springer-Verlag
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Mayer-Wolf, E., Nualart, D., Pérez-Abreu, V. (1992). Large deviations for multiple Wiener-Itô integral processes. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXVI. Lecture Notes in Mathematics, vol 1526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084307
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DOI: https://doi.org/10.1007/BFb0084307
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