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math.PR2024★ 1 cited
Fractional Ito Calculus for Randomly Scaled Fractional Brownian Motion and its Applications to Evolution Equations
Yana A. Butko, Merten Mlinarzik
We define a fractional Ito stochastic integral with respect to a randomly scaled fractional Brownian motion via an -transform approach. We investigate the properties of this sto…
math.PR2024
Limit Theorems for the Dynamical Foundation of the Fractional Brownian Motion and Related Models of Anomalous Diffusion with Random Diffusion Coefficient and Time-Dependent Random Hurst parameter
Christian Bender, Yana A. Butko, Mirko D'Ovidio +1
Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most r…