CONFIGURATION SPACES FOR SELF-SIMILAR RANDOM PROCESSES, AND MEASURES QUASI-INVARIANT UNDER DIFFEOMORPHISM GROUPS

2000 ◽  
pp. 228-242 ◽  
Author(s):  
GERALD A. GOLDIN
Keyword(s):  
Random Processes ◽  
Configuration Spaces ◽  
Diffeomorphism Groups ◽  
Self Similar

scholarly journals Self-similar random processes and infinite-dimensional configuration spaces

2005 ◽  
Vol 68 (10) ◽  
pp. 1675-1684 ◽  
Author(s):  
G. A. Goldin ◽  
U. Moschella ◽  
T. Sakuraba
Keyword(s):  
Random Processes ◽  
Configuration Spaces ◽  
Infinite Dimensional ◽  
Self Similar

Is Network Traffic Self-Similar or Multifractal?

Fractals ◽  
1997 ◽  
Vol 05 (01) ◽  
pp. 63-73 ◽  
Author(s):  
Murad S. Taqqu ◽  
Vadim Teverovsky ◽  
Walter Willinger
Keyword(s):  
Network Traffic ◽  
Local Area Network ◽  
Local Area ◽  
Random Processes ◽  
Wide Area ◽  
Area Network ◽  
Wide Area Network ◽  
Packet Network ◽  
Self Similar ◽  
Traffic Measurements

This paper addresses the question of whether self-similar processes are sufficient to model packet network traffic, or whether a broader class of multifractal processes is needed. By using the absolute moments of aggregate traffic measurements, we conclude that measured local-area network (LAN) and wide-area network (WAN) traffic traces, with the sample means subtracted, are well modeled by random processes that are either exactly or asymptotically self-similar.

BASIC PROPERTIES AND CHARACTERIZATION OF STOCHASTICALLY SELF-SIMILAR PROCESSES IN Rd

Fractals ◽  
1999 ◽  
Vol 07 (01) ◽  
pp. 59-78 ◽  
Author(s):  
DANIELE VENEZIANO
Keyword(s):  
Random Variable ◽  
Random Processes ◽  
Affine Transformations ◽  
Spectral Measures ◽  
Self Similarity ◽  
Basic Properties ◽  
Properties And Characterization ◽  
Classical Notion ◽  
Self Similar

The classical notion of self-similarity (ss) for random X(t) as invariance under the group of positive affine transformations {X→ arX, t→rt; ar>0} is extended by allowing ar to be a random variable. The resulting property of "stochastic self-similarity" (sss) is applied to both ordinary and generalized random processes in Rd, d≥1. The class of sss processes seems to correspond to that of multifractal processes (the latter are variously defined in the literature). The spectral measures of ordinary and generalized sss processes are themselves stochastically self-similar. Two characterizations of ss processes by Lamperti are extended to the sss case and several basic properties of ordinary and generalized sss processes are derived.

ENGINEERING APPLICATIONS OF FRACTIONAL BROWNIAN MOTION: SELF-AFFINE AND SELF-SIMILAR RANDOM PROCESSES

Fractals ◽  
1999 ◽  
Vol 07 (02) ◽  
pp. 151-157 ◽  
Author(s):  
P. S. ADDISON ◽  
A. S. NDUMU
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Random Processes ◽  
The Other ◽  
Engineering Applications ◽  
Self Similar ◽  
Diffusive Processes ◽  
Spatial Trajectories

The purpose of this paper is to explain the connection between fractional Brownian motion (fBm) and non-Fickian diffusive processes, and at the same time, highlight three engineering applications: two requiring self-affine fBm trace functions and the other requiring self-similar fBm spatial trajectories.

scholarly journals Estimation of stopping times for stopped self-similar random processes

2021 ◽  
Author(s):  
Viktor Schulmann
Keyword(s):  
Brownian Motion ◽  
Convergence Rate ◽  
Asymptotic Normality ◽  
Mellin Transform ◽  
Random Processes ◽  
Random Time ◽  
Stopping Times ◽  
Bessel Processes ◽  
One Dimensional ◽  
Self Similar

AbstractLet $$X=(X_t)_{t\ge 0}$$ X = ( X t ) t ≥ 0 be a known process and T an unknown random time independent of X. Our goal is to derive the distribution of T based on an iid sample of $$X_T$$ X T . Belomestny and Schoenmakers (Stoch Process Appl 126(7):2092–2122, 2015) propose a solution based the Mellin transform in case where X is a Brownian motion. Applying their technique we construct a non-parametric estimator for the density of T for a self-similar one-dimensional process X. We calculate the minimax convergence rate of our estimator in some examples with a particular focus on Bessel processes where we also show asymptotic normality.

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