Fractional Stochastic Models for Heavy Tailed, and Long-Range Dependent, Fluctuations in Physical Systems

2017 ◽  
pp. 340-368 ◽  
Author(s):  
Nicholas W. Watkins
Keyword(s):  
Long Range ◽  
Stochastic Models ◽  
Physical Systems ◽  
Heavy Tailed

On modelling physical systems with stochastic models: diffusion versus Lévy processes

2008 ◽  
Vol 366 (1875) ◽  
pp. 2455-2474 ◽  
Author(s):  
Cécile Penland ◽  
Brian D Ewald
Keyword(s):  
Differential Equations ◽  
Stochastic Models ◽  
Lévy Processes ◽  
Numerical Models ◽  
Gaussian White Noise ◽  
Levy Processes ◽  
Physical Systems ◽  
Random Forcing ◽  
Weather And Climate ◽  
Made In

Stochastic descriptions of multiscale interactions are more and more frequently found in numerical models of weather and climate. These descriptions are often made in terms of differential equations with random forcing components. In this article, we review the basic properties of stochastic differential equations driven by classical Gaussian white noise and compare with systems described by stable Lévy processes. We also discuss aspects of numerically generating these processes.

On Long-Range Dependence in Regenerative Processes Based on a General ON/OFF Scheme

2007 ◽  
Vol 44 (02) ◽  
pp. 379-392
Author(s):  
Remigijus Leipus ◽  
Donatas Surgailis
Keyword(s):  
Closed Form ◽  
Long Range ◽  
Covariance Function ◽  
Queueing System ◽  
Regenerative Process ◽  
Long Range Dependence ◽  
Exact Asymptotics ◽  
Regenerative Processes ◽  
Service Times ◽  
Heavy Tailed

In this paper, we obtain a closed form for the covariance function of a general stationary regenerative process. It is used to derive exact asymptotics of the covariance function of stationary ON/OFF and workload processes, when ON and OFF periods are heavy-tailed and mutually dependent. The case of a G/G/1/0 queueing system with heavy-tailed arrival and/or service times is studied in detail.

Topological mechanics of knots and tangles

Science ◽  
2020 ◽  
Vol 367 (6473) ◽  
pp. 71-75 ◽  
Author(s):  
Vishal P. Patil ◽  
Joseph D. Sandt ◽  
Mathias Kolle ◽  
Jörn Dunkel
Keyword(s):  
Long Range ◽  
Mechanical Stability ◽  
Spin Systems ◽  
Physical Systems ◽  
Mechanical Deformations ◽  
Counting Rules ◽  
Turbulent Plasmas

Knots play a fundamental role in the dynamics of biological and physical systems, from DNA to turbulent plasmas, as well as in climbing, weaving, sailing, and surgery. Despite having been studied for centuries, the subtle interplay between topology and mechanics in elastic knots remains poorly understood. Here, we combined optomechanical experiments with theory and simulations to analyze knotted fibers that change their color under mechanical deformations. Exploiting an analogy with long-range ferromagnetic spin systems, we identified simple topological counting rules to predict the relative mechanical stability of knots and tangles, in agreement with simulations and experiments for commonly used climbing and sailing bends. Our results highlight the importance of twist and writhe in unknotting processes, providing guidance for the control of systems with complex entanglements.

Stochastic approximation with long range dependent and heavy tailed noise

2012 ◽  
Vol 71 (1-2) ◽  
pp. 221-242 ◽  
Author(s):  
V. Anantharam ◽  
V. S. Borkar
Keyword(s):  
Long Range ◽  
Stochastic Approximation ◽  
Heavy Tailed

scholarly journals Long range dependence of heavy-tailed random functions

2021 ◽  
Vol 58 (3) ◽  
pp. 569-593
Author(s):  
Rafal Kulik ◽  
Evgeny Spodarev
Keyword(s):  
Long Range ◽  
Random Function ◽  
Limit Theorems ◽  
Random Processes ◽  
Long Range Dependence ◽  
Infinite Variance ◽  
Random Functions ◽  
Heavy Tailed ◽  
Definition Of ◽  
Index Space

AbstractWe introduce a definition of long range dependence of random processes and fields on an (unbounded) index space $T\subseteq \mathbb{R}^d$ in terms of integrability of the covariance of indicators that a random function exceeds any given level. This definition is specifically designed to cover the case of random functions with infinite variance. We show the value of this new definition and its connection to limit theorems via some examples including subordinated Gaussian as well as random volatility fields and time series.

scholarly journals Buffer content of a leaky-bucket system with long-range dependent input traffic

2003 ◽  
Vol 40 (3) ◽  
pp. 581-601
Author(s):  
Bárbara González-Arévalo ◽  
Gennady Samorodnitsky
Keyword(s):  
Flow Control ◽  
Long Range ◽  
Long Range Dependence ◽  
Single Server ◽  
Finite Buffer ◽  
Input Stream ◽  
Leaky Bucket ◽  
Expected Time ◽  
Fluid Queues ◽  
Heavy Tailed

The leaky bucket is a flow control mechanism that is designed to reduce the effect of the inevitable variability in the input stream into a node of a communication network. In this paper we study what happens when an input stream with heavy-tailed work sessions arrives to a server protected by such a leaky bucket. Heavy-tailed sessions produce long-range dependence in the input stream. Previous studies of single server fluid queues without flow control suggested that such long-range dependence can have a dramatic effect on the system performance. By concentrating on the expected time till overflow of a large finite buffer we show that leaky-bucket flow control does make the system overflow less often, but long-range dependence still makes its presence felt.

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