Discrete approximation of symmetric jump processes on metric measure spaces

Zhen Qing Chen; Panki Kim; Takashi Kumagai

doi:10.1007/s00440-012-0411-x

Discrete approximation of symmetric jump processes on metric measure spaces

Zhen Qing Chen, Panki Kim^*, Takashi Kumagai

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a large class of symmetric jump processes. We also discuss some application of our results to the scaling limit of random walk in random conductance.

Original language	English
Pages (from-to)	703-749
Number of pages	47
Journal	Probability Theory and Related Fields
Volume	155
Issue number	3-4
DOIs	https://doi.org/10.1007/s00440-012-0411-x
Publication status	Published - Apr 2013
Externally published	Yes

Keywords

Dirichlet form
Jump process
Mosco convergence
Random conductance
Skorohod space
Symmetric jump process
Tightness
Weak convergence

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10.1007/s00440-012-0411-x

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abstract = "In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a large class of symmetric jump processes. We also discuss some application of our results to the scaling limit of random walk in random conductance.",

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AB - In this paper we give general criteria on tightness and weak convergence of discrete Markov chains to symmetric jump processes on metric measure spaces under mild conditions. As an application, we investigate discrete approximation for a large class of symmetric jump processes. We also discuss some application of our results to the scaling limit of random walk in random conductance.

KW - Dirichlet form

KW - Jump process

KW - Mosco convergence

KW - Random conductance

KW - Skorohod space

KW - Symmetric jump process

KW - Tightness

KW - Weak convergence

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IS - 3-4

ER -

Discrete approximation of symmetric jump processes on metric measure spaces

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Keywords

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