ISSN:
1432-0606
Keywords:
RKHS
;
Tensor products
;
Sobolev derivative
;
Generalized chaos expansions
;
60G30
;
60H10
;
60H99
;
58G32
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01371087
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