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Integral representation of generalized grey Brownian motion
Wolfgang Bock1, Sascha Desmettre2, José Luís da Silva3
1Department of Mathematics, TU Kaiserslautern (TUK), Kaiserslautern, Germany.
Abstract:
In this paper, we investigate the representation of a class of non-Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular, the underlying process can be seen as a non-Gaussian extension of the Ornstein-Uhlenbeck process, hence generalizing the representation results of Muravlev, Russian Math. Surveys 66 (2), 2011 as well as Harms and Stefanovits, Stochastic Process. Appl. 129, 2019 to the non-Gaussian case.
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