A cascade decomposition theory with applications to Markov and exchangeable cascades

DOI10.1090/S0002-9947-96-01500-0zbMath0857.60028OpenAlexW1895238018MaRDI QIDQ4875714

Stanley C. Williams, Edward C. Waymire

Publication date: 13 June 1996

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-96-01500-0

zbMATH Keywords

momentsHausdorff dimensionsupportcascades

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Geometric probability and stochastic geometry (60D05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Continuity and singularity of induced measures (60G30) Foundations of stochastic processes (60G05) Exchangeability for stochastic processes (60G09)

Related Items (22)

Branching within branching: a model for host-parasite co-evolution ⋮ Seneta-Heyde norming in the branching random walk ⋮ Measure change in multitype branching ⋮ Scaling exponents and multifractal dimensions for independent random cascades ⋮ Some width function asymptotics for weighted trees ⋮ Multifractal scaling of products of birth-death processes ⋮ Size-biased branching population measures and the multi-type \(x \log x\) condition ⋮ Multifractal analysis of infinite products of stationary jump processes ⋮ A general decomposition theory for random cascades ⋮ Trigonometric multiplicative chaos and applications to random distributions ⋮ On Markov-Mandelbrot martingales ⋮ Multifractal analysis in a mixed asymptotic framework ⋮ Multiperiodic multifractal martingale measures. ⋮ LARGE DEVIATIONS OF MULTIFRACTAL MEASURES ⋮ Limit theorems for multiplicative cascades in a random environment ⋮ Limsup deviations on trees ⋮ Turbulent cascades: Limitations and a statistical test of the lognormal hypothesis ⋮ Uniform convergence for complex [0,1-martingales] ⋮ Convergence of complex multiplicative cascades ⋮ Tree Polymers in the Infinite Volume Limit at Critical Strong Disorder ⋮ Independent random cascades on Galton-Watson trees ⋮ Statistical estimation for multiplicative cascades.

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