Title :
On the linear structure of self-similar processes
Author :
Nuzman, Carl J. ; Poor, H. Vincent
Author_Institution :
Dept. of Electr. Eng., Princeton Univ., NJ, USA
Abstract :
Self-similar processes have a rich linear structure, based on scale invariance, which is analogous to the shift-invariant structure of stationary processes. The analogy is made explicit via Lamperti´s (1962) transformation. This transformation is used here to characterize the reproducing kernel Hilbert space (RKHS) associated with self-similar processes and hence to solve problems of prediction, whitening, and Gaussian signal detection. Some specific results for the fractional Brownian motion illustrate the general concepts
Keywords :
Brownian motion; Gaussian processes; Hilbert spaces; prediction theory; signal detection; stochastic processes; transforms; white noise; Gaussian signal detection; Lamperti transformation; RKHS; fractional Brownian motion; linear structure; prediction; reproducing kernel Hilbert space; scale invariance; self-similar processes; shift-invariant structure; stationary processes; whitening; Brownian motion; Electrical engineering; Finance; Hilbert space; Hydrology; Kernel; Physics; Random variables; Signal detection; Stochastic processes;
Conference_Titel :
Information Theory, 2000. Proceedings. IEEE International Symposium on
Conference_Location :
Sorrento
Print_ISBN :
0-7803-5857-0
DOI :
10.1109/ISIT.2000.866796
