Semilinear fractional stochastic differential equations driven by a $\gamma$ -Hölder continuous signal with $\gamma>2 / 3$

León, Jorge A.Márquez, David (Márquez Carreras)2020-04-172020-12-3120190219-4937https://hdl.handle.net/2445/155665In 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) $333-374]$application/pdfeng(c) World Scientific Publishing, 2019Equacions integrals estocàstiquesProcessos de moviment browniàEquacions integralsStochastic integral equationsBrownian motion processesIntegral equationsSemilinear fractional stochastic differential equations driven by a $\gamma$ -Hölder continuous signal with $\gamma>2 / 3$info:eu-repo/semantics/article6978742020-04-17info:eu-repo/semantics/openAccess