Two classes of self-similar stable processes with stationary increments

DOI10.1016/0304-4149(89)90082-3zbMath0713.60050OpenAlexW1972615957MaRDI QIDQ750004

Makoto Maejima, Stamatis Cambanis

Publication date: 1989

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(89)90082-3

zbMATH Keywords

domain of attractionself-similar symmetric stable processes with stationary increments

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Stochastic processes (60G99) Self-similar stochastic processes (60G18)

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Cites Work

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• Log-fractional stable processes
• On path properties of certain infinitely divisible processes
• Sample path properties of self-similar processes with stationary increments
• Limit theorems for sums of linearly generated random variables
• Spectral density estimation for stationary stable processes
• Convergence of quadratic forms in p-stable random variables and \(\theta _ p\)-radonifying operators
• On Itô stochastic integration with respect to p-stable motion: Inner clock, integrability of sample paths, double and multiple integrals
• Weighted sums of i.i.d. random variables attracted to integrals of stable processes
• Some path properties of pth order and symmetric stable processes
• On the spectral representation of symmetric stable processes
• The L p Norm of Sums of Translates of a Function
• Prediction of stable processes: Spectral and moving average representations
• Limit theorems for non-linear functionals of Gaussian sequences
• On a class of self-similar processes
• Infinite variance self-similar processes subordinate to a poisson measure
• A self-similar process with nowhere bounded sample paths
• Random measures and harmonizable sequences