Tóm tắt: I am going to present the content of my PhD thesis “Stochastic differential equations driven by fractional Brownian motions”. Fractional Brownian motion is considered a natural candidate to model the noise in mathematical finance, hydrology, communication networks and in other fields. In the last decade, stochastic differential equations driven by fractional Brownian motions (in short fSDE) have attracted a lot of research interest. This dissertation focuses on studying the nonautonomous fSDE with Hurst index H > 1/2 form dx_t = f(t, x_t)dt + g(t, x_t)dB^H_t, where f , g are time dependent coefficient functions. The topics included are
- The existence and uniqueness of the solution and solution’s properties.
- Lyapunov spectrum of linear system.
- Random attractor of the system.
