23 citations · 73 across the 8 of their papers we have counts for
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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…
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…
Subordination principle and Feynman-Kac formulae for generalized time-fractional evolution equations
Christian Bender, Marie Bormann, Yana A. Butko
We consider generalized time-fractional evolution equations of the form with a fairly general memory kernel and an operator being the gen…
Stochastic solutions of generalized time-fractional evolution equations
Christian Bender, Yana A. Butko
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-fracti…
Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equations
Yana A. Butko
Semigroups, generated by Feller processes killed upon leaving a given domain, are considered. These semigroups correspond to Cauchy-Dirichlet type initial-exterior value problems i…
Chernoff approximation of subordinate semigroups and applications
Yana A. Butko
In this note the Chernoff Theorem is used to approximate evolution semigroups constructed by the procedure of subordination. The considered semigroups are subordinate to some origi…
Lagrangian and Hamiltonian Feynman formulae for some Feller semigroups and their perturbations
Yana A. Butko, René L. Schilling, Oleg G. Smolyanov
A Feynman formula is a representation of a solution of an initial (or initial-boundary) value problem for an evolution equation (or, equivalently, a representation of the semigroup…