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math.PR2026
Scaling limits of Lévy walks with random velocities
Hubert Woszczek, Marek A. Teuerle, Agnieszka Wyłomańska
This paper investigates Lévy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depe…
math.PR2024
Riemann-Liouville fractional Brownian motion with random Hurst exponent
Hubert Woszczek, Agnieszka Wylomanska, Aleksei Chechkin
We examine two stochastic processes with random parameters, which in their basic versions (i.e., when the parameters are fixed) are Gaussian and display long range dependence and a…
math.PR2024
Scaled Brownian motion with random anomalous diffusion exponent
Hubert Woszczek, Aleksei Chechkin, Agnieszka Wylomanska
The scaled Brownian motion (SBM) is regarded as one of the paradigmatic random processes, featuring the anomalous diffusion property characterized by the diffusion exponent. It is…