scholarly journals Representations of hermite processes using local time of intersecting stationary stable regenerative sets

2020 ◽  
Vol 57 (4) ◽  
pp. 1234-1251
Author(s):  
Shuyang Bai
Keyword(s):  
Long Range ◽  
Local Time ◽  
Limit Theorems ◽  
Local Times ◽  
Long Range Dependence ◽  
Random Interval ◽  
Stationary Increments ◽  
Self Similar ◽  
Regenerative Sets

AbstractHermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

Large deviations, moderate deviations, and queues with long-range dependent input

1999 ◽  
Vol 31 (1) ◽  
pp. 254-278 ◽  
Author(s):  
Cheng-Shang Chang ◽  
David D. Yao ◽  
Tim Zajic
Keyword(s):  
Brownian Motion ◽  
Long Range ◽  
Sample Path ◽  
Transient Behavior ◽  
Moderate Deviations ◽  
Long Range Dependence ◽  
Standard Process ◽  
Liouville Type ◽  
Stationary Increments ◽  
Moderate Deviations Principle

Long-range dependence has been recently asserted to be an important characteristic in modeling telecommunications traffic. Inspired by the integral relationship between the fractional Brownian motion and the standard Brownian motion, we model a process with long-range dependence, Y, as a fractional integral of Riemann-Liouville type applied to a more standard process X—one that does not have long-range dependence. When X takes the form of a sample path process with bounded stationary increments, we provide a criterion for X to satisfy a moderate deviations principle (MDP). Based on the MDP of X, we then establish the MDP for Y. Furthermore, we characterize, in terms of the MDP, the transient behavior of queues when fed with the long-range dependent input process Y. In particular, we identify the most likely path that leads to a large queue, and demonstrate that unlike the case where the input has short-range dependence, the path here is nonlinear.

scholarly journals On the generation of self-similar with long-range dependent traffic using piecewise affine chaotic one-dimensional maps (renewed version-2)

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Long Range ◽  
Hurst Exponent ◽  
Long Range Dependence ◽  
One Dimensional ◽  
Temporal Series ◽  
Qualitative And Quantitative ◽  
Piecewise Affine ◽  
Proposed Model ◽  
Self Similar ◽  
One Dimensional Maps

A qualitative and quantitative extension of the chaotic models used to generate self-similar traffic with long-range dependence (LRD) is presented by means of the formulation of a model that considers the use of piecewise affine one-dimensional maps. Based on the disaggregation of the temporal series generated, a valid explanation of the behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

scholarly journals MULTIVARIATE LIMIT THEOREMS IN THE CONTEXT OF LONG-RANGE DEPENDENCE

2013 ◽  
Vol 34 (6) ◽  
pp. 717-743 ◽  
Author(s):  
Shuyang Bai ◽  
Murad S. Taqqu
Keyword(s):  
Long Range ◽  
Limit Theorems ◽  
Long Range Dependence

scholarly journals Self-similar processes in collective risk theory

1998 ◽  
Vol 11 (4) ◽  
pp. 429-448 ◽  
Author(s):  
Zbigniew Michna
Keyword(s):  
Long Range ◽  
Risk Model ◽  
Queueing Systems ◽  
Risk Process ◽  
Risk Theory ◽  
Similar Process ◽  
Long Range Dependence ◽  
Insurance Company ◽  
Collective Risk ◽  
Self Similar

Collective risk theory is concerned with random fluctuations of the total assets and the risk reserve of an insurance company. In this paper we consider self-similar, continuous processes with stationary increments for the renewal model in risk theory. We construct a risk model which shows a mechanism of long range dependence of claims. We approximate the risk process by a self similar process with drift. The ruin probability within finite time is estimated for fractional Brownian motion with drift. A similar model is applicable in queueing systems, describing long range dependence in on/off processes and associated fluid models. The obtained results are useful in communication network models, as well as storage and inventory models.

scholarly journals Ordinal Pattern Dependence in the Context of Long-Range Dependence

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 670
Author(s):  
Ines Nüßgen ◽  
Alexander Schnurr
Keyword(s):  
Time Series ◽  
Long Range ◽  
Limit Theorems ◽  
Long Range Dependence ◽  
Limit Distributions ◽  
Ordinal Information ◽  
Dependence Measure ◽  
Multivariate Dependence ◽  
Ordinal Time Series ◽  
Ordinal Pattern

Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the dependence between the two processes. This article deals with ordinal pattern dependence for a long-range dependent time series including mixed cases of short- and long-range dependence. We investigate the limit distributions for estimators of ordinal pattern dependence. In doing so, we point out the differences that arise for the underlying time series having different dependence structures. Depending on these assumptions, central and non-central limit theorems are proven. The limit distributions for the latter ones can be included in the class of multivariate Rosenblatt processes. Finally, a simulation study is provided to illustrate our theoretical findings.

scholarly journals On the generation of self-similar with long-range dependent traffic using piecewise affine chaotic one-dimensional maps (renewed version)

2021 ◽  
Author(s):  
Ginno Millán
Keyword(s):  
Long Range ◽  
Hurst Exponent ◽  
Long Range Dependence ◽  
One Dimensional ◽  
Temporal Series ◽  
Qualitative And Quantitative ◽  
Piecewise Affine ◽  
Proposed Model ◽  
Self Similar ◽  
One Dimensional Maps

A qualitative and quantitative extension of the chaotic models used to generate self-similar traffic with long-range dependence (LRD) is presented by means of the formulation of a model that considers the use of piecewise affine one-dimensional maps. Based on the disaggregation of the temporal series generated, a valid explanation of the behavior of the values of Hurst exponent is proposed and the feasibility of their control from the parameters of the proposed model is shown.

Sign in / Sign up

Export Citation Format

Share Document