Fractional Ito Calculus for Randomly Scaled Fractional Brownian Motion and its Applications to Evolution Equations
arXiv:2412.14397 · doi:10.1007/s10959-026-01484-7
Abstract
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 stochastic integral, prove the Ito formula for functions of such stochastic integrals and apply this Ito formula for investigation of related generalized time-fractional evolution equations.
References in corpus (14)
- Anomalous transport in the crowded world of biological cells
- Anomalous dynamics of cell migration
- Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
- Characterizations and simulations of a class of stochastic processes to model anomalous diffusion
- Non-Markovian diffusion equations and processes: analysis and simulations
- Fractional kinetics emerging from ergodicity breaking in random media
- Transient superdiffusion and long-range correlations in the motility patterns of trypanosomatid flagellate protozoa
- Mittag-Leffler Analysis I: Construction and characterization
- Superstatistical modelling of protein diffusion dynamics in bacteria
- Integral Representation of Generalized Grey Brownian Motion
- Grey Brownian motion local time: Existence and weak-approximation
- Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations
- Stochastic solutions of generalized time-fractional evolution equations
- Form Factors for Generalized Grey Brownian Motion