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 class of infinite-dimensional Gaussian processes defined through generalized fractional operators
The generalization of fractional Brownian motion in infinite-dimensional white and grey
noise spaces has been recently carried over, following the Mandelbrot-Van Ness …
noise spaces has been recently carried over, following the Mandelbrot-Van Ness …
Non-Gaussian measures in infinite dimensional spaces: the gamma-grey noise
In the context of non-Gaussian analysis, Schneider introduced grey noise measures, built
upon Mittag-Leffler functions; analogously, grey Brownian motion and its generalizations …
upon Mittag-Leffler functions; analogously, grey Brownian motion and its generalizations …
[HTML][HTML] A class of processes defined in the white noise space through generalized fractional operators
The generalization of fractional Brownian motion in the white and grey noise spaces has
been recently carried over, following the Mandelbrot–Van Ness representation, through …
been recently carried over, following the Mandelbrot–Van Ness representation, through …
Stochastic analysis for vector-valued generalized grey Brownian motion
In this article, we show that the standard vector-valued generalization of a generalized grey
Brownian motion (ggBm) has independent components if and only if it is a fractional …
Brownian motion (ggBm) has independent components if and only if it is a fractional …
Great Barrier Reef degradation, sea surface temperatures, and atmospheric CO2 levels collectively exhibit a stochastic process with memory
ARB Elnar, CB Cena, CC Bernido… - Climate Dynamics, 2021 - Springer
Quantifying ecological memory could be done at several levels from the rate of physiological
changes in an ecosystem all the way down to responses at the genetic level. One way of …
changes in an ecosystem all the way down to responses at the genetic level. One way of …
Generalized white noise analysis and topological algebras
In this paper we develop a framework to extend the theory of generalized stochastic
processes in the Hida white noise space to more general probability spaces which include …
processes in the Hida white noise space to more general probability spaces which include …
Characterization and analysis of generalized grey incomplete gamma noise
W Bock, L Cristofaro - Stochastics, 2024 - Taylor & Francis
The grey incomplete gamma distributions was established by one of the authors in a
previous publication. In this article we use the Kondratiev characterization theorem to …
previous publication. In this article we use the Kondratiev characterization theorem to …
Fractional Ito Calculus for Randomly Scaled Fractional Brownian Motion and its Applications to Evolution Equations
YA Butko, M Mlinarzik - arXiv preprint arXiv:2412.14397, 2024 - arxiv.org
We define a fractional Ito stochastic integral with respect to a randomly scaled fractional
Brownian motion via an $ S $-transform approach. We investigate the properties of this …
Brownian motion via an $ S $-transform approach. We investigate the properties of this …
Appell system associated with the infinite dimensional Fractional Pascal measure
In this work, we employ a biorthogonal approach to construct the infinite-dimensional
Fractional Pascal measure μ σ (α), 0< α≤ 1, defined on the tempered distributions space …
Fractional Pascal measure μ σ (α), 0< α≤ 1, defined on the tempered distributions space …