Stable Processes with Stationary Increments Parameterized by Metric Spaces

Zuopeng Fu () and Yizao Wang ()
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Zuopeng Fu: University of Cincinnati
Yizao Wang: University of Cincinnati

Journal of Theoretical Probability, 2020, vol. 33, issue 3, 1737-1754

Abstract: Abstract A new family of stable processes indexed by metric spaces with stationary increments is introduced. They are special cases of a new family of set-indexed stable processes with Chentsov representation. At the heart of the representation, a result on the so-called measure definite kernels is of independent interest. A limit theorem for set-indexed processes is also established.

Keywords: Lévy Brownian field; Set-indexed process; Stable process; Stationary increment; Chentsov representation; Measure definite kernel; 60G22; 60G52; 60G60 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00912-1

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