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Title: Semilinear fractional stochastic differential equations driven by a $\gamma$ -Hölder continuous signal with $\gamma>2 / 3$
Author: León, Jorge A.
Márquez, David (Márquez Carreras)
Keywords: Equacions integrals estocàstiques
Processos de moviment brownià
Equacions integrals
Stochastic integral equations
Brownian motion processes
Integral equations
Issue Date: 2019
Publisher: World Scientific Publishing
Abstract: In this paper, we use the techniques of fractional calculus to study the existence of a unique solution to semilinear fractional differential equation driven by a $\gamma$ -Hölder continuous function $\theta$ with $\gamma \in\left(\frac{2}{3}, 1\right) .$ Here, the initial condition is a function that may not be defined at zero and the involved integral with respect to $\theta$ is the extension of the Young integral [An inequality of the Hölder type, connected with Stieltjes integration, Acta Math.67 (1936) 251-282] given by Zähle [Integration with respect to fractal functions and stochastic calculus I, Probab. Theory Related Fields111 (1998) $333-374]$
Note: Versió postprint del document publicat a:
It is part of: Stochastics and Dynamics, 2019
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ISSN: 0219-4937
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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