Peter E. Kloeden, University of Tuebingen

Jialin Hong, Professor

The Euler Scheme for Caputo Fractional Stochastic Differential Equations

16:00-17:00 June 30 (Thursday), ZOOM ID: 974 5774 8545

We construct and investigate an Euler-Maruyama type scheme for Caputo stochastic fractional differential equations (for short Caputo SFDE) of order $\alpha$ $\in$ $(1⁄2, 1)$ with coefficients satisfying standard Lipschitz and linear growth bound conditions. The strong convergence rate of this scheme is established. In particular, it is $\alpha -1⁄2$ when the coefficients of the SFDE are independent of time. In addition, the convergence and stability of an exponential Euler-Maruyama scheme for bilinear scalar Caputo SFDEs is considered.