Measurable Riemannian structures associated with strong local Dirichlet forms |
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Authors: | Masanori Hino |
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Institution: | 1. +81 2. 75 3. 753 4. 3378+81 5. 3381;6. Graduate School of Informatics, Kyoto University, , Kyoto, 606‐8501 Japan |
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Abstract: | We introduce Riemannian‐like structures associated with strong local Dirichlet forms on general state spaces. Such structures justify the principle that the pointwise index of the Dirichlet form represents the effective dimension of the virtual tangent space at each point. The concept of differentiations of functions is studied, and an application to stochastic analysis is presented. |
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Keywords: | Dirichlet form measurable Riemannian structure energy measure index diffusion process martingale additive functional 31C25 46G05 60J60 60H05 |
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