COMPUTER EXPERIMENTS WITH FRACTIONAL GAUSSIAN NOISES .3. MATHEMATICAL APPENDIX

The present ‘Appendix’ is devoted to mathematical considerations designed to fill in the innumerable logical gaps left in the preceding paper. Even though most proofs will be merely sketched or omitted, the notation remains heavy, and some readers may wish to skip to formulas 1 and 2, which define ‘Type 1 functions.’ Most of what follows is closely patterned after Mandelbrot and Van Ness [1968], which contains additional mathematical details and references to the few earlier articles, where fractional Gaussian noises were fleetingly considered as purely mathematical entities. Copyright 1969 by the American Geophysical Union.