Journal ArticleDOI
Mittag-Leffler's function and stochastic linear Volterra equations of convolution type
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TLDR
In this paper, the authors considered the class of stochastic linear Volterra equations of convolution type defined by fractional integration kernels g ρ (t)={ 1 Γ(ρ) }t ρ−1, ρ∈(0,2) using an explicit formula for the scalar resolvent function.Abstract:
We consider the class of stochastic linear Volterra equations of convolution type defined by fractional integration kernels g ρ (t)={ 1 Γ(ρ) }t ρ−1, ρ∈(0,2) Using an explicit formula for the scalar resolvent function, we establish the basic properties of the stochastic convolution process W S Our formulas are given in terms of the Mittag-Leffler's functionread more
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On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension
Latifa Debbi,Marco Dozzi +1 more
TL;DR: In this paper, the existence, uniqueness and regularity of the trajectories of mild solutions of one-dimensional nonlinear stochastic fractional partial differential equations of order α > 1 containing derivatives of entire order and perturbed by space-time white noise are studied.
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Equivalence of Volterra processes
Fabrice Baudoin,David Nualart +1 more
TL;DR: In this article, necessary and sufficient conditions for the equivalence of Volterra Gaussian processes were studied and new proofs, precisions and new theorems for equivalence were provided.
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Sharp Gaussian regularity on the circle, and applications to the fractional stochastic heat equation
TL;DR: In this paper, a sharp regularity theory for homogeneous Gaussian fields on the unit circle is established and two types of characterizations for such a field to have a given almost-sure uniform modulus of continuity are established in a general setting.
Journal Article
Convolution type stochastic Volterra equations
TL;DR: In this paper, the authors present a survey of the work of Prof. Michal Kisielewicz, Uniwersytet Zielonogorski Prof. dr hab. Leszek Slominski and Dr. Aleksander Weron.
References
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Book
Evolutionary integral equations and applications
TL;DR: In this article, the authors deal with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space, where the main feature of the kernels involved is that they consist of unbounded linear operators.
Book
Nonlinear Volterra integral equations
TL;DR: The nonlinear volterra integral equations is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.
Journal ArticleDOI
The completely monotonic character of the Mittag-Leffler function $E_a \left( { - x} \right)$
Journal ArticleDOI
Integrodifferential equation which interpolates the heat equation and the wave equation
TL;DR: In this article, the integrodifferential equation (IDE) is decomposed by its decomposition for every α, 1≤α≤2 and α = 2.
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