4 problems

Let $(X,d,m,\mathcal E,\mathcal F)$ be an MMD space. Suppose it satisfies sub-Gaussian heat kernel estimates with volume growth exponent $\alpha$ and walk dimension $\beta$, and le…

Let $(X,d,m,\mathcal E,\mathcal F)$ be an MMD space, meaning a metric measure Dirichlet space equipped with the associated diffusion. Suppose it satisfies sub-Gaussian heat kernel…

Let a diffusion on a metric measure space have spectral dimension, and let its martingale dimension be defined as the dimension of its martingale representation. Hino proved that f…

Let ${\mathbf F}=\{{\mathcal F}_t\}_{t\in[0,\infty)}$ be the filtration induced by the canonical diffusion process on a nested fractal. An AF-martingale dimension of one means that…