Green Measures for a Class of Non-Markov Processes

Herry P. Suryawan and José L. da Silva ()
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Herry P. Suryawan: Department of Mathematics, Sanata Dharma University, Yogyakarta 55281, Indonesia
José L. da Silva: CIMA, Faculty of Exact Sciences and Engineering, University of Madeira, Campus da Penteada, 9020-105 Funchal, Portugal

Mathematics, 2024, vol. 12, issue 9, 1-8

Abstract: In this paper, we investigate the Green measure for a class of non-Gaussian processes in R d . These measures are associated with the family of generalized grey Brownian motions B β , α , 0 < β ≤ 1 , 0 < α ≤ 2 . This family includes both fractional Brownian motion, Brownian motion, and other non-Gaussian processes. We show that the perpetual integral exists with probability 1 for d α > 2 and 1 < α ≤ 2 . The Green measure then generalizes those measures of all these classes.

Keywords: fractional Brownian motion; generalized grey Brownian motion; green measure; subordination (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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