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Self-Affine Processes and the Ergodic Theorem

Published online by Cambridge University Press:  20 November 2018

Wim Vervaat
Wim Vervaat*
Affiliation:
Mathématiques Université Claude Bernard Lyon 1 43, Boulevard du 11 Novembre 1918 69622 Villeurbanne cedex France e-mail:, vervaat@jonas.univ-lyonl.fr
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Abstract

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Known results for strictly stable motions as finiteness of moments and local boundednessof sample-path variation are generalized to self-affine processes, i.e., self-similar processes with stationary increments. The proofs are new, even for stable motions, and are obtained by applying the ergodic theorem to powers of the (one-sided) increments.

Keywords

60G1860G17self-similar processself-affine processstable motionbounded variation of sample paths
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 2 , 01 June 1994 , pp. 254 - 262
Copyright
Copyright © Canadian Mathematical Society 1994

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