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Semilinear fractional stochastic differential equations driven by a $\gamma$ -Hölder continuous signal with $\gamma>2 / 3$
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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) $333-374]$
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LEÓN, Jorge A. and MÁRQUEZ, David (Márquez Carreras). Semilinear fractional stochastic differential equations driven by a $\gamma$ -Hölder continuous signal with $\gamma>2 / 3$. Stochastics and Dynamics. 2019. ISSN 0219-4937. [consulted: 8 of October of 2026]. Available at: https://hdl.handle.net/2445/155665