The reproducing kernel Hilbert space structure of the sample paths of a Gaussian process

@article{Driscoll1973TheRK,
  title={The reproducing kernel Hilbert space structure of the sample paths of a Gaussian process},
  author={Michael F. Driscoll},
  journal={Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und Verwandte Gebiete},
  year={1973},
  volume={26},
  pages={309-316}
}
  • M. Driscoll
  • Published 1973
  • Mathematics
  • Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
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References

SHOWING 1-10 OF 10 REFERENCES
Continuity Properties of Some Gaussian Processes
Zero-one laws for Gaussian processes
Some zero-one laws are proved for Gaussian processes defined on linear spaces of functions. They are generalizations of a result for Wiener measure due to R. H. Cameron and R. E. Graves. The proofsExpand
On the continuity of stationary Gaussian processes
Let us consider a stochastically continuous, separable and measurable stationary Gaussian process X = { X ( t ), − ∞ t ∞ } with mean zero and with the covariance function p ( t ) = EX ( t + s ) X ( sExpand
Convergence of Random Processes and Limit Theorems in Probability Theory
The convergence of stochastic processes is defined in terms of the so-called “weak convergence” (w. c.) of probability measures in appropriate functional spaces (c. s. m. s.).Chapter 1. Let $\Re $ beExpand
A theory of cross-spaces
Theory of Reproducing Kernels.
Abstract : The present paper may be considered as a sequel to our previous paper in the Proceedings of the Cambridge Philosophical Society, Theorie generale de noyaux reproduisants-Premiere partieExpand