On Positive Definite Kernels, Related Problems and Applications

• R. Bruzual ^[1] ; A. de la Barrera ^[2] ; M. Domínguez ^[1]
  1. [1] Universidad Central de Venezuela

     Universidad Central de Venezuela

     Venezuela

     
  2. [2] Universidad de Pamplona

     Universidad de Pamplona

     Colombia

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 29, Nº 1-2, 2014, págs. 97-115
• Idioma: inglés
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• Resumen

  • We give a representation result for regular positive definite Toeplitz kernels and, as a corollary, we obtain a representation result for equivalent kernels. We obtain a stability result which is used to show that, under certain conditions, a special perturbation of a positive definite Toeplitz kernel is equivalent to the perturbed kernel. Some applications to stochastic processes are given.