• Corpus ID: 119650407

Spectral theory for Gaussian processes: Reproducing kernels, random functions, boundaries, and $\mathbf L^2$-wavelet generators with fractional scales

  title={Spectral theory for Gaussian processes: Reproducing kernels, random functions, boundaries, and \$\mathbf L^2\$-wavelet generators with fractional scales},
  author={Daniel Alpay and Palle E. T. Jorgensen},
  journal={arXiv: Functional Analysis},
A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by a host of applications, e.g., in mathematical physics, and in stochastic differential equations, and their use in financial models. In this paper, we show that, for three classes of cases in the correspondence, it is possible to obtain explicit formulas… 
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