Analysis on local Dirichlet spaces

By Peter K. Friz, Nicolas Victoir. 2010

279 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2bf2011ef625db22c4c768b26c916e06900ce0b8

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Neumann and Dirichlet Heat Kernels in Inner Uniform Domains (2011, background): “Sturm, the equivalence between –”
Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, unknown): “In the framework of strictly local regular Dirichlet spaces with a complete intrinsic metric, the following two properties are equivalent [28, 57]: (i) The heat kernel satisfies c′ 1 exp{− c1ρ 2(x,y) t } √ μ(B(x, √ t))μ(B(y, √ t)) ≤ pt(x, y) ≤ c ′ 2 exp{− c2ρ 2(x,y) t } √ μ(B(x, √ t))μ(B(y, √ t)) (1”
An Overview of the Proof of the Splitting Theorem in Spaces with Non-Negative Ricci Curvature (2014, background): “In particular, from the general results obtained by Sturm in [48], [49], we get the existence of a mass preserving heat kernel satisfying Gaussian estimates, i.”
Multidimensional Stochastic Processes as Rough Paths: Theory and Applications (2010, background): “17 (Localized lower heat kernel bounds) [159] Assume E is a strongly local, strongly regular Dirichlet form on (2) () which satisfies (I),(II),(III).”
The Li-Yau Inequality and Heat Kernels on Metric Measure Spaces (2014, result): “Hence, the results from Sturm [41, 42] imply that there existsC := C(N,K) (C := C(N), if K ≥ 0) such that, for eacht ≤ 1 (resp. allt > 0) and all x, y ∈ X, it holds that C−1µ(B(x, √ t))−1/2µ(B(y, √ t))−1/2 exp { −d(x, y) 2 C2t } ≤ p(t, x, y) ≤ Cµ(B(x, √ t))−1/2µ(B(y, √ t))−1/2 exp { − d(x, y)2 C1t }”
Dirichlet forms and stochastic completeness of graphs and subgraphs (2009, unknown): “They are true for general Dirichlet forms and can, for example, be found in the works [24], [25].”
Conservation property of symmetric jump processes (2011, unknown): “Utilizing the following inequality (which takes place of the chain rule for a localoperator [21]): ∣∣ga(x) − ga(y)∣∣ ≤ aeaga(x)∣∣r(x) − r(y)∣∣, x, y ∈ X with ∣∣r(x) − r(y)∣∣ ≤ 1, and taking into account that |r(x) − r(y)| ≤ d(x, y), we have”