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Decomposition of Gaussian processes, and factorization of positive definite kernels. (English) Zbl 1443.47085

This well-written paper is concerned with an integrated approach to positive definite kernels and Gaussian processes, with an emphasis on factorizations and their applications. The main contribution is an explicit duality for positive definite functions (kernels) on the one hand, and Gaussian processes (in terms of Ito-integration) on the other.
The paper is complemented by a number of instructive examples, applications and motivations.

MSC:

47L60 Algebras of unbounded operators; partial algebras of operators
46N30 Applications of functional analysis in probability theory and statistics
46N50 Applications of functional analysis in quantum physics
42C15 General harmonic expansions, frames
65R10 Numerical methods for integral transforms
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C75 Structural characterization of families of graphs
31C20 Discrete potential theory
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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