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Variational Principles for Asymptotic Variance of General Markov Processes
A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get an upper bound of the mean exit...
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Probabilistic Characterization of Weakly Harmonic Maps with Respect to Non-Local Dirichlet Forms
We characterize weakly harmonic maps with respect to non-local Dirichlet forms by Markov processes and martingales. In particular, we can obtain...
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On the Restriction of a Right Process Outside a Negligible Set
The objective of this paper is to examine the restriction of a right process on a Radon topological space, excluding a negligible set, and...
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Parabolic Harnack Inequality Implies the Existence of Jump Kernel
We prove that the parabolic Harnack inequality implies the existence of jump kernel for symmetric pure jump process. This allows us to remove a...
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On the Upper Rate Functions of Some Time Inhomogeneous Diffusion Processes
In the present paper, we study an upper escape rate of some time inhomogeneous diffusion process associated with a family of regular and local...
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Time Regularity for Local Weak Solutions of the Heat Equation on Local Dirichlet Spaces
We study the time regularity of local weak solutions of the heat equation in the context of local regular symmetric Dirichlet spaces. Under two basic...
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An Averaging Principle for Stochastic Flows and Convergence of Non-Symmetric Dirichlet Forms
We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on a manifold. Using...