Foundations and TrendsŪ in Stochastic Systems
LONG RANGE DEPENDENCE
by Gennady Samorodnitsky (Cornell University, USA)
Long Range Dependence is a wide ranging survey of the ideas, models and techniques associated with the notion of long memory. It begins with a historical survey going back to W Hurst and the Nile river data, and goes on to discuss the various traditional and new points of view on long range dependence. These include connections with non-stationary processes, with ergodic theory, with self-similar processes and with fractionally difference processes. The survey considers the implications of long memory on stochastic models with heavy tails and light tails, on processes defined as stochastic integrals, single and multiple, on limit theorems and on large deviations.
Long Range Dependence will serve as an invaluable reference source for researchers studying long range dependence, for those building long memory models, and for people who are trying to detect the possible presence of long memory in data.
Published by Now Publishers and marketed by World Scientific
Contents:
- Introduction
- Some History. The Hurst Phenomenon
- Long Memory and
Non-Stationarity
- Long Memory, Ergodic Theory and Strong Mixing
- Second-Order Theory
- Fractional Processes and Related Models with Long Memory
- Self-Similar Processes
- Long Range Dependence as a Phase Transition
- References
Readership: Postgraduates and researchers in mathematics, computer science and
operations research.
| 104pp |
Pub. date: Dec 2007 |
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