Abstract
Let (i, H, B) be an abstract Wiener space and let W ɛ be the associated semigroup of gaussian measures on B; let f be a function mapping H into another Banach space E.
Suppose that there exists an increasing sequence P
n
of finite dimensional projections, converging strongly to identity, such that f(
) converges in the measure W
ɛ to 
.
We give some sufficient conditions to ensure that the family of measures 
is a large deviations system in the sense of Varadhan. We show that the Varadhan contraction principle works in this case, as if the cylinder gaussian measures on H were real measures.
This research was partially supported by the AFOSR Grant 87-0136 while the second named author was visiting the University of Tennessee, Knoxville. The author wishes to thank Professors Balram S. Rajput and Jan Rosiński for their warm hospitality.
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© 1989 Springer-Verlag
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Smoleński, W., Sztencel, R. (1989). Large deviations for non-linear radonifications of white noise. In: Da Prato, G., Tubaro, L. (eds) Stochastic Partial Differential Equations and Applications II. Lecture Notes in Mathematics, vol 1390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083951
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DOI: https://doi.org/10.1007/BFb0083951
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