Martingale dimensions for fractals

DOI10.1214/07-AOP349zbMath1144.60046arXiv0711.2135MaRDI QIDQ2427054

Masanori Hino

Publication date: 15 May 2008

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.2135

zbMATH Keywords

Dirichlet formsfractalsself-similar setsDavis-Varaiya invariantmartingale dimensionmultiplicity of filtration

Mathematics Subject Classification ID

Dirichlet forms (31C25) Martingales with continuous parameter (60G44) Diffusion processes (60J60) Fractals (28A80)

Related Items (13)

Backward problems for stochastic differential equations on the Sierpinski gasket ⋮ Some properties of energy measures on Sierpinski gasket type fractals ⋮ Indices of Dirichlet forms ⋮ Upper estimate of martingale dimension for self-similar fractals ⋮ Estimates of the Local Spectral Dimension of the Sierpinski Gasket ⋮ Vector analysis for Dirichlet forms and quasilinear PDE and SPDE on metric measure spaces ⋮ Local behavior of smooth functions for the energy Laplacian on the Sierpinski gasket ⋮ Geodesic distances and intrinsic distances on some fractal sets ⋮ Sup-norm-closable bilinear forms and Lagrangians ⋮ Approximation of partial differential equations on compact resistance spaces ⋮ On the viscous Burgers equation on metric graphs and fractals ⋮ Parabolic type equations associated with the Dirichlet form on the sierpinski gasket ⋮ Measurable Riemannian structures associated with strong local Dirichlet forms

Cites Work

• Unnamed Item
• Unnamed Item
• Dirichlet forms of fractals and products of random matrices
• Dirichlet forms and analysis on Wiener space
• The multiplicity of an increasing family of \(\sigma\)-fields
• Statistical mechanics and fractals
• Dirichlet forms and symmetric Markov processes
• On singularity of energy measures on self-similar sets
• On a class of additive functionals of Markov processes
• ON SINGULARITY OF ENERGY MEASURES ON SELF-SIMILAR SETS II
• Brownian motion on nested fractals

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