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Stationary covariances associated with exponentially convex functions. (English) Zbl 1045.60032

Bernoulli 9, No. 4, 607-615 (2003); acknowledgement of priority ibid. 10, No. 2, 375 (2004).
The authors establish a bijective mapping between exponentially convex functions and positively definite functions, and extend Loève’s construction of stochastic processes associated with them. As an application, they derive parametric covariance model for locally stationary random fields.

MSC:

60G10 Stationary stochastic processes
60G60 Random fields
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