A01=Paul Embrechts
Almost surely
Approximation
Asymptotic analysis
Author_Paul Embrechts
Autocorrelation
Autoregressive conditional heteroskedasticity
Autoregressive-moving-average model
Availability
Benoit Mandelbrot
Brownian motion
Category=PBWL
Central limit theorem
Change of variables
Computational problem
Confidence interval
Correlogram
Covariance matrix
Data analysis
Data set
Determination
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Fixed point (mathematics)
Foreign exchange market
Fractional Brownian motion
Gaussian process
Heavy-tailed distribution
Heuristic method
Inference
Infimum and supremum
Instance (computer science)
Internet traffic
Joint probability distribution
Likelihood function
Limit (mathematics)
Linear regression
Log-log plot
Marginal distribution
Mathematica
Mathematical finance
Mathematics
Methodology
Mixture model
Model selection
Normal distribution
Parametric model
Power law
Probability theory
Publication
Random variable
Regime
Renormalization
Self-similar process
Self-similarity
Simulation
Spectral density
Square root
Stable distribution
Stable process
Stationary process
Stationary sequence
Statistical inference
Statistical physics
Statistics
Stochastic calculus
Stochastic process
Technology
Telecommunication
Textbook
Theorem
Time series
Variance
Wavelet
Website
Product details
- ISBN 9780691096278
- Weight: 340g
- Dimensions: 152 x 235mm
- Publication Date: 05 Aug 2002
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
The modeling of stochastic dependence is fundamental for understanding random systems evolving in time. When measured through linear correlation, many of these systems exhibit a slow correlation decay--a phenomenon often referred to as long-memory or long-range dependence. An example of this is the absolute returns of equity data in finance. Selfsimilar stochastic processes (particularly fractional Brownian motion) have long been postulated as a means to model this behavior, and the concept of selfsimilarity for a stochastic process is now proving to be extraordinarily useful. Selfsimilarity translates into the equality in distribution between the process under a linear time change and the same process properly scaled in space, a simple scaling property that yields a remarkably rich theory with far-flung applications. After a short historical overview, this book describes the current state of knowledge about selfsimilar processes and their applications. Concepts, definitions and basic properties are emphasized, giving the reader a road map of the realm of selfsimilarity that allows for further exploration.
Such topics as noncentral limit theory, long-range dependence, and operator selfsimilarity are covered alongside statistical estimation, simulation, sample path properties, and stochastic differential equations driven by selfsimilar processes. Numerous references point the reader to current applications. Though the text uses the mathematical language of the theory of stochastic processes, researchers and end-users from such diverse fields as mathematics, physics, biology, telecommunications, finance, econometrics, and environmental science will find it an ideal entry point for studying the already extensive theory and applications of selfsimilarity.
Paul Embrechts is Professor of Mathematics at the Swiss Federal Institute of Technology (ETHZ), Zurich, Switzerland. He is the author of numerous scientific papers on stochastic processes and their applications and the coauthor of the influential book on "Modelling of Extremal Events for Insurance and Finance". Makoto Maejima is Professor of Mathematics at Keio University, Yokohama, Japan. He has published extensively on selfsimilarity and stable processes.
