In this paper we introduce a definition of a multi-dimensional fractional Brownian motion of Hurst index H ∈ (0, 1) under volatility uncertainty (in short G-fBm). We study the properties of such a process and provide first results about stochastic calculus with respect to a multi- dimensional G-fBm for a Hurst index H ∈ ( 1 , 1).
Multi-dimensional fractional Brownian motion in the G-setting
Mazzon, A
;Oberpriller, K
2025-01-01
Abstract
In this paper we introduce a definition of a multi-dimensional fractional Brownian motion of Hurst index H ∈ (0, 1) under volatility uncertainty (in short G-fBm). We study the properties of such a process and provide first results about stochastic calculus with respect to a multi- dimensional G-fBm for a Hurst index H ∈ ( 1 , 1).
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