Monatshefte für Mathematik

, Volume 188, Issue 1, pp 87–107 | Cite as

Stochastic mappings and random distribution fields: A correlation approach

  • Păstorel GaşparEmail author
  • Lorena Popa


This paper contains a study of multivariate (infinite dimensional) second order stochastic mappings indexed by an abstract set \(\Lambda \) in close connection to their operator covariance functions. The characterizations of the normal Hilbert module or of Hilbert spaces associated to such a multivariate second order stochastic mapping in terms of reproducing kernel structures are given, aiming not only to gather into a unified manner some concepts from the field, but also to identify a way to obtain a fundamental extension of the very well elaborated theory of multivariate second order stochastic processes, or random fields, to the case of multivariate second order random distribution fields, including multivariate second order stochastic measures. Finally a general Wold type decomposition is extended and discussed in this framework.


Stochastic mappings Correlation function Positive definite kernels Reproducing kernel Hilbert modules Kolmogorov factorization Stochastic measures Random distribution fields 

Mathematics Subject Classification

60G20 47B32 


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Authors and Affiliations

  1. 1.Department of Mathematics and Computer Science, Faculty of Exact Sciences“Aurel Vlaicu” University, AradAradRomania

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