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September 2019 Distribution flows associated with positivity preserving coercive forms
Xian Chen, Zhi-Ming Ma, Xue Peng
Ann. Probab. 47(5): 2894-2929 (September 2019). DOI: 10.1214/18-AOP1327

Abstract

For a given quasi-regular positivity preserving coercive form, we construct a family of ($\sigma$-finite) distribution flows associated with the semigroup of the form. The canonical cadlag process equipped with the distribution flows behaves like a strong Markov process. Moreover, employing distribution flows we can construct optional measures and establish Revuz correspondence between additive functionals and smooth measures. The results obtained in this paper will enable us to perform a kind of stochastic analysis related to positivity preserving coercive forms.

Citation

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Xian Chen. Zhi-Ming Ma. Xue Peng. "Distribution flows associated with positivity preserving coercive forms." Ann. Probab. 47 (5) 2894 - 2929, September 2019. https://doi.org/10.1214/18-AOP1327

Information

Received: 1 January 2017; Revised: 1 November 2018; Published: September 2019
First available in Project Euclid: 22 October 2019

zbMATH: 07145306
MathSciNet: MR4021240
Digital Object Identifier: 10.1214/18-AOP1327

Subjects:
Primary: 31C25, 47D03
Secondary: 31C15, 60J40, 60J45

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 5 • September 2019
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