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G. Kallianpur (1979)
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GW Johnson, G Kallianpur (1989)
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G Kallianpur (1980)
Applications of Mathematics, Vol. 13
Malliavin calculus has been extensively developed for abstract Wiener spaces. It is of interest to develop the basic concepts of an infinite-dimensional calculus for an arbitrary Gaussian processX=(Xt), wheret $$ \in$$ T (T being a multiparameter set or, more generally, a complete separable metric space), bringing into evidence the properties of the covariance kernel (or, equivalently, the reproducing kernel Hilbert space) ofX. In this paper a definition of thekth Sobolev derivative is given and thekth chaos expansion of a functional is shown to be thekth-order divergence operator. An extension of Itô's decomposition formula is derived.
Applied Mathematics and Optimization – Springer Journals
Published: Mar 10, 2005
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