Symmetric Markov Processes, Time Change, and Boundary Theory

By Zhen-Qing Chen, 福島 正俊. 2011

443 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/868364dd0f2368981a21278f792fb9d8badf93dc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Luigi Ambrosio
2. Vadim Linetsky
3. Giuseppe Savar'e
4. Likuan Qin
5. Xicheng Zhang
6. Gianluca Crippa
7. Pierre-Emmanuel Jabin
8. Camillo De Lellis

In Management Science and Operations Research

1. Vadim Linetsky
2. Giuseppe Savar'e
3. Likuan Qin

Citations in the corpus

• Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces (2015, background): “rtant property (see e.g. [8, Remark 6.3]) is that Eis regular, i.e. V∩Cc(X) is dense both in V(w.r.t. the Vnorm) and in Cc(X) (w.r.t. the uniform norm). In particular, by Fukushima’s theory (see e.g. [25, 17]), every ϕ∈ V admits a E-quasi continuous representative ˜ϕuniquely determined up to E-polar”
• Long Term Risk: A Martingale Approach (2014, methodology): “hen Pt = Pˆt, i.e. the pricing operators are symmetric with respect to the measure m, (Pt)t≥0 can be interpreted as the transition semigroup of a symmetric Markov process Xr killed at the rate r (cf. Chen and Fukushima (2011) and Fukushima et al. (2010)). In particular, essentially all one-dimension”
• Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in $RCD (K, \infty)$ metric measure spaces (2013, background): “ts and E-polar sets can also be characterized in terms of capacities; we recall here a version that we will be useful later on. The capacity Cap (it corresponds to Caph,1 with h≡ 1 in the notation of [19]) of an open set A⊂ Xis defined by Cap(A) := inf kuk2 V : u≥ 1 m-a.e. in A , and it can be extend”
• Stability of elliptic Harnack inequality (2016, background): “uence of Lemma 7.5 and Theorem 7.6. We conclude this paper by suggesting a characterization of the EHI in terms of capacity, or equivalently effective conductance. Let Dbe a bounded domain in X. As in [CF] we can define a reflected Dirichlet space Fe D; the associated diffusion Xeis the process X reflect”