TITLE

Tree indexed Markov processes and long range dependency

AUTHOR(S)
White, Langford B.; Perreau, Sylvie L.
PUB. DATE
March 2000
SOURCE
AIP Conference Proceedings;2000, Vol. 511 Issue 1, p353
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
This paper describes the second order statistics of a finite state Markov process indexed on a binary tree. Such models are the discrete state analogues of the continuous state Gauss-Markov processes as described by Basseville et al. [1]. Such processes are termed tree-indexed processes. The idea is to use the leaf nodes of the tree at a specified depth, as indices for a time series, and to derive a probabilistic model for this time series. The paper shows that such processes possess covariance functions which decay as a power law thus exhibiting a long range dependent (LRD) or self-similarity property. These models are motivated in part by recent evidence that suggests some communications network traffic may exhibit such behavior. However, the processes are highly non-stationary in nature. The paper poses as an open question whether there exists a modification of the tree structure which permits the leaf node process to be stationary but retains the LRD property. © 2000 American Institute of Physics.
ACCESSION #
6029559

 

Related Articles

  • Csiszar's divergences for testing the order in a Markov chain. Menendez, M.L.; Pardo, J.A.; Pardo, L. // Statistical Papers;2001, Vol. 42 Issue 3, p313 

    Discusses the testing of a Markov chain of order on the basis of divergences in the statistical information theory. Characterization of the order of the chain; Formulation of the Markov chain with positive transition probabilities; Proof associated with the analysis of the chain.

  • A new strong optimality criterion for nonstationary Markov decision processes. Guo, Xianping; Shi, Peng; Zhu, Weiping // Mathematical Methods of Operations Research;2000, Vol. 52 Issue 2, p287 

    This paper deals with a new optimality criterion consisting of the usual three average criteria and the canonical triplet (totally so-called strong average-canonical optimality criterion) and introduces the concept of a strong average-canonical policy for nonstationary Markov decision processes,...

  • Modelling Hierarchical Systems by a Continuous-Time Homogeneous Markov Chain Using Two-Wave Panel... Carette, Philippe // Journal of Applied Probability;Sep99, Vol. 36 Issue 3, p644 

    Presents information on a study which investigated the effect of sampling variability to open hierarchical system by a continuous-time homogeneous Markov chain using. Application of a two panel-wave panel data in the sampling variability; Methodology of the study; Discussion of the result;...

  • ON THE CORRELATION STRUCTURE OF UNILATERAL AR PROCESSES ON THE PLANE. Champagnat, F.; Idier, J. // Advances in Applied Probability;Jun2000, Vol. 32 Issue 2, p408 

    Studies the correlation structures of quarter-plane autoregressive (AR) processes and unilateral AR process. Relation to Pickard-type property; Assessment of correlation matching and maximum entropy properties; Role of Pickard property in providing the missing equations that complement the...

  • BAYESIAN INFERENCE FOR MARKOV CHAINS. Eichelsbacher, Peter; Ganesh, Ayalvadi // Journal of Applied Probability;Mar2002, Vol. 39 Issue 1, p91 

    Presents a study that investigated the estimation of Markov transition matrices by Bayesian methods. Background on the Bayesian approach to inference in applied statistics; Analysis of an irreducible, discrete Markov chain with a finite state space; Discussion on large and moderate deviation...

  • Spatial analysis in a Markov random field framework: The case of burning oil wells in Kuwait. Dezzani, Raymond J.; Al-Dousari, Ahmad // Journal of Geographical Systems;Dec2001, Vol. 3 Issue 4, p387 

    This paper discusses a modeling approach for spatial-temporal prediction of environmental phenomena using classified satellite images. This research was prompted by the analysis of change and landscape redistribution of petroleum residues formed from the residue of the burning oil wells in...

  • Bayesian analysis of Markov Modulated Bernoulli Processes. �zekici, S.; Soyer, R. // Mathematical Methods of Operations Research;2003, Vol. 57 Issue 1, p125 

    We consider Markov Modulated Bernoulli Processes (MMBP) where the success probability of a Bernoulli process evolves over time according to a Markov chain. The MMBP is applied in reliability modeling where systems and components function in a randomly changing environment. Some of these...

  • On mean reward variance in semi-Markov processes. Sladk�, Karel // Mathematical Methods of Operations Research;2005, Vol. 62 Issue 3, p387 

    As an extension of the discrete-time case, this note investigates the variance of the total cumulative reward for the embedded Markov chain of semi-Markov processes. Under the assumption that the chain is aperiodic and contains a single class of recurrent states recursive formulae for the...

  • Statistical analysis of transfer of fluctuations in solar wind turbulence. Strumik, M.; Macek, W. M. // Nonlinear Processes in Geophysics;2008, Vol. 15 Issue 4, p607 

    We present results of statistical analysis of the transfer of fluctuations in solar wind turbulence. We investigate the dynamics of the slow solar wind using an approach based on the Markov processes theory and experimental data measured by ACE spacecraft. In particular, we test whether the...

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics