Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations
C Bender, M Bormann, YA Butko - Fractional Calculus and Applied …, 2022 - Springer
We consider a class of generalized time-fractional evolution equations containing a fairly
general memory kernel k and an operator L being the generator of a strongly continuous …
general memory kernel k and an operator L being the generator of a strongly continuous …
Stochastic solutions of generalized time-fractional evolution equations
C Bender, YA Butko - Fractional Calculus and Applied Analysis, 2022 - Springer
We consider a general class of integro-differential evolution equations which includes the
governing equation of the generalized grey Brownian motion and the time-and space …
governing equation of the generalized grey Brownian motion and the time-and space …
A Limit Theorem Clarifying the Physical Origin of Fractional Brownian Motion and Related Gaussian Models of Anomalous Diffusion
We consider a dynamical system describing the motion of a test-particle surrounded by $ N
$ Brownian particles with different masses. Physical principles of conservation of momentum …
$ Brownian particles with different masses. Physical principles of conservation of momentum …
Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles
Complex systems are known to display anomalous diffusion, whose signature is a
space/time scaling with in the probability density function (PDF). Anomalous diffusion can …
space/time scaling with in the probability density function (PDF). Anomalous diffusion can …
Time-changed fractional Ornstein-Uhlenbeck process
We define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional
Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of …
Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of …
Stochastic bridges over ensemble of linear systems
We consider particles that are conditioned to initial and final states. The trajectory of these
particles is uniquely shaped by the intricate interplay of internal and external sources of …
particles is uniquely shaped by the intricate interplay of internal and external sources of …
On the model of random walk with multiple memory structure
NS Arkashov - Physica A: Statistical Mechanics and its Applications, 2022 - Elsevier
A model of one-dimensional random walk based on the memory flow phenomenology is
constructed. In this model, the jumps of the random walk process have a convolution …
constructed. In this model, the jumps of the random walk process have a convolution …
Linear combinations of iid strictly stable variables with random coefficients and their application to anomalous diffusion processes
We show that linear combinations of independent and identically distributed strictly stable
variables with positive random coefficients is equal in distribution to a function of these …
variables with positive random coefficients is equal in distribution to a function of these …
Generalized Fokker–Planck equation for superstatistical systems
C Runfola, G Pagnini - Physica D: Nonlinear Phenomena, 2024 - Elsevier
Superstatistical systems are non-equilibrium systems in stationary states with large
fluctuations of intensive quantities. Different effective statistical processes follow accordingly …
fluctuations of intensive quantities. Different effective statistical processes follow accordingly …
Integral representation of generalized grey Brownian motion
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 …
namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic …