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      Upper estimate of martingale dimension for self-similar fractals

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          Abstract

          We study upper estimates of the martingale dimension \(d_m\) of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that \(d_m=1\) for natural diffusions on post-critically finite self-similar sets and that \(d_m\) is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.

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          Most cited references16

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          On Square Integrable Martingales

          Theory of real and time continuous martingales has been developed recently by P. Meyer [8, 9]. Let be a square integrable martingale on a probability space P. He showed that there exists an increasing process ‹X›t such that
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            Function Spaces and Potential Theory

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              Dirichlet forms on fractals and products of random matrices

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                Author and article information

                Journal
                25 May 2012
                2012-06-19
                Article
                10.1007/s00440-012-0442-3
                1205.5617
                7b41b84c-5fa7-4ae3-bfbd-d63b8bdac228

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                60G44, 28A80, 31C25, 60J60
                Probab. Theory Related Fields 156 (2013), 739-793
                49 pages, 7 figures; minor revision with adding a reference
                math.PR

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