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Dirichlet forms and symmetric Markov processes
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The article was published on 1994-01-01 and is currently open access. It has received 1613 citations till now. The article focuses on the topics: Hierarchical Dirichlet process & Generalized Dirichlet distribution.read more
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Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
TL;DR: In this article, the authors provide an overview of the properties of the Brownian motion on complete non-compact Riemannian manifolds as recurrence and non-explosion.
Journal ArticleDOI
Metric measure spaces with Riemannian Ricci curvature bounded from below
TL;DR: In this article, a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X,d,m) is introduced, which is stable under measured Gromov-Hausdorff convergence and rules out Finsler geometries.
Journal ArticleDOI
Heat kernel estimates for stable-like processes on d-sets
Zhen-Qing Chen,Takashi Kumagai +1 more
TL;DR: In this paper, stable-like processes on d-sets are investigated, which include reflected stable processes in Euclidean domains as a special case, and a sharp two-sided heat kernel estimate for such processes is derived.
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Gaussian processes: Inequalities, small ball probabilities and applications
Wenbo V. Li,Qi-Man Shao +1 more
TL;DR: In this paper, the authors focus on the inequalities, small-ball probabilities, and application of Gaussian processes, and find that the small ball probability is a key step in studying the lower limits of the Gaussian process.