Let F be a square integrable random variable on the classical Wiener space and let us denote by fn the symmetric kernels appearing in its chaos expansion. We give sufficient conditions for the unambiguous definition of F at the points of the Cameron Martin space. We also give conditions for the existence of approximate limits (in the sense of Denjoy). These results are first proved for multiple integrals In(fn) before they are extended to the general random variables F. The conditions are given in terms of the Lp-norms of the kernels fn. The last section of the paper is devoted to an original application of our estimates to the proof of the existence of the Onsager-Machlup functional for a nonanticipative stochastic differential equation of a special type.
|Original language||English (US)|
|Number of pages||37|
|Journal||Journal of Functional Analysis|
|State||Published - Aug 1 1992|
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